As Olympic swimmers this week prepare to dive into the River Seine in Paris, a long-polluted urban river, Boston’s Charles River is getting closer to making its own public debut.

“We’re not there yet,’’ said Max Rome, the stormwater program manager at the Charles River Watershed Association. “But we’re in the ballpark.’’

For decades, the Charles has been a punch line, its “Dirty Water’’ memorialized in a rock song and known as something most would consider jumping in only on a dare. On the Esplanade Thursday, Jacob Casper, 20, who grew up in Brookline, joked that he might “grow a second head’’ if he took a plunge.

Will Spangenberg, 26, has more love for the Charles, which flows through his hometown of Dover. Now a Beacon Hill resident, he visits the river three or four times a week to sail, paddle board, or just hang out. He regularly falls into the water or gets wet while boating.

Yet the water has “a hint of green that I’m not in love with,’’ Spangenberg acknowledged while sunbathing on a dock near Longfellow Bridge. “But I’m never worried about it. And if it’s 90 degrees and I’m paddle boarding, I’ll take the risk.’’

Reputation aside, the Charles is actually cleaner than the Seine in terms of E. coli bacterial contamination from waste water runoff and old sewer-to-river connections, even though Paris spent more than $1 billion to clean the river before hosting the Olympics.

“We’ve been ahead of Paris,’’ Rome said, who compared the water quality data between the two rivers and has studied remediation of urban rivers. “A lot of what they did to prepare for the Olympics was kind of basic stuff. In our area, we’ve already done many of the things they’ve done quite recently.’’

Last week, Paris Mayor Anne Hidalgo swam in the Seine, wearing a full wetsuit and goggles, to demonstrate the river was now clean enough for Olympic athletes.

But a similar stunt was pulled here some 28 years ago when then-Governor Bill Weld famously leapt into the Charles River, fully clothed, during a signing ceremony for a state law to protect rivers from new development.

Four centuries of urbanization and industrialization made the Charles one of the most polluted bodies of water in America (at one time, waste was intentionally conveyed directly to the river, according to the EPA). After almost three decades of efforts by federal, state, and local authorities to reverse that pollution, water quality has improved, data show. Still, the long-held goal to make the Charles consistently safe for swimming and fishing remains just out of reach — a disappointment to longtime residents and newcomers alike.

“I’ve heard awful things’’ about the water, said Natalie Szumel, 26, a therapist reading a book on a Charles River dock on Friday. When she first relocated to Boston from Baltimore earlier this year, she wanted to swim in the river but was told by a friend, “No, that’s not what we do here.’’

Public beaches on the Charles were closed to swimmers in 1949 with a state permit. (Swimming in the Seine was banned to the public in 1923.)

Now 75 years later, Rome, the water quality expert, thinks that samples from the Charles look good enough to begin planning for when to reopen beaches.

It depends on how the next couple years go, Rome said. “We’re in a cautious, but optimistic moment.’’

With the Olympics bringing more attention to river swimming, it’s a good time for local leaders to begin considering the future of the Charles, he said.

“I think it’s time to start a civic conversation about swimming in the river,’’ Rome said. “I don’t think people realize how close we are to being able to do that today.’’

According to water-quality samples taken in June and July from the Charles near the Longfellow Bridge and from the Seine at the Pont Alexandre III in Paris, the Seine had more than 30 times the concentration of E. coli bacteria than in the Charles.

E. coli is a type of bacteria commonly found in feces and can make people very sick with vomiting and diarrhea.

Technically, the area of the Seine where marathon swimming and the triathlon will occur would not be considered swimmable by US Environmental Protection Agency recommendations.

The Olympics are using a much less rigorous standard to evaluate water quality for the swimmers than federal and Massachusetts standards.

For the Olympics, water samples with the highest 10 percent of E. coli concentrations can contain no more than an average of 900 colony-forming units of E. coli per 100 milliliters, according to the World Triathlon Federation’s criteria. The US EPA, by comparison, recommends no more than 410 colony- forming units of E. coli per 100 millimeters in the highest samples, while Massachusetts is even more conservative. Here, the water is not considered safe for swimming if any sample is higher than 235.

So, by the standards used by the Olympics, the Charles River could almost certainly host the Games, and the water at the Longfellow Bridge would be considered of “excellent quality’’; the Seine, meanwhile, is considered “sufficient.’’

When and where the Charles could become safe under Massachusetts standards for regular public swimming, however, is a different question. Right near the Museum of Science, for example, the Charles is safe to swim in much of the time, data show, but not all the time. Other areas further upstream, such as near Boston University, are more prone to bacteria contamination.

Also, the river may be unsafe for at least 48 hours after heavy rains, due to bacteria and other pollutants, said EPA spokesperson Jo Anne Kittrell.

That’s because rains bring urban street contamination, such as dog waste, gushing into the river, and heavy rains can also overwhelm old combined stormwater and sewage systems in Massachusetts, causing rainwater to mix with wastewater, which flows into the river. The Seine in Paris has similar problems.

According to the Massachusetts Water Resource Authority, combined sewage overflows in the Charles have decreased by 99 percent since the 1980s, although there is “more work to be done,’’ said Sean Navin, a spokesperson for the agency.

The Charles has the added wrinkle of being prone to harmful cyanobacterial algal blooms, caused by an excess of nutrients, warm temperatures, and slow-moving water. Those algal blooms can release toxins in the water that cause skin rashes and long-term liver, kidney, and central nervous system problems. It’s also toxic to pets.

However, Rome said the Charles has not experienced a major algal bloom in three years, the longest stretch of time without one.

The river appears to be turning a corner and cleanup efforts are beginning to show promising results, he said. At least one swimming event, City Splash at the Esplanade, is held annually.

But that’s just one day a year.

Should Boston host the Olympics and let the athletes swim the Charles? Spangenberg, the sunbather full of Boston pride, said yes.

“I love that dirty water,’’ he said, a reference to The Standells’ 1966 rock song about Boston. “but I’m glad to see it’s getting cleaner.’’

Globe correspondent Rachel Umansky-Castro contributed to this report.

Erin Douglas can be reached at erin.douglas@globe.com. Follow her @erinmdouglas23.