As Loui Eriksson walked out of the TD Garden just after 11 a.m. on Sunday, the question still remained: In what capacity would he walk in again? Would it be as a player traded elsewhere? As a member of the Bruins for the long haul? As a still-in-limbo-impending unrestricted free agent?

On Sunday evening, he remained what he had been: a member of the Boston Bruins.

He had walked back in that afternoon still a member of a team that — according to general manager Don Sweeney — wanted to sign him. And, more than that, he played on Sunday night in a 4-1 loss to the Lightning, a crucial matchup between teams fighting for playoff positioning in the Atlantic Division.

Eriksson, for one, did not want to discuss his future on Sunday morning after he took part in the Bruins’ morning skate alongside his teammates.

“I don’t really want to talk about that right now,’’ Eriksson said, when asked about his level of optimism regarding getting a deal negotiated with the Bruins. “We’ll see what’s going to happen. All I can do is just play and just help the team, like I’ve been saying the last couple times I’ve talked to you guys.’’

But that isn’t exactly an easy thing to do.

“It’s obviously a lot of things going around,’’ he said. “Coming back to it again, I’m just trying to play the game and have fun with the team and try to win games right now.’’

Meanwhile, Sweeney and Eriksson’s agent, J.P. Barry, have been engaged in contract talks, but the two sides remain separated by a gap that could signal the end of the winger’s time in Boston.

“We’ve made offers to Loui and haven’t been able to find a deal at this point in time,’’ Sweeney said in a press conference at 5 p.m. “It’s sort of status quo on that front.’’

He added, “There’s been ongoing discussions. Certainly they have their position and we have ours. I’d like to find a deal, but it hasn’t happened until this point.’’

Sweeney was clear that he would like to keep Eriksson, but with the 30-year-old winger hitting unrestricted free agency this summer and with this likely to be his final major deal, it’s not a surprise that his camp is pushing for more. It’s not a surprise, either, that the Bruins would be wary of adding more term and more dollars, given the uncertainty surrounding the salary cap and the need to lock up players in subsequent years (like, say, Brad Marchand).

The question is where the Bruins will go if this deal doesn’t get done, whether the Bruins would feel the need to trade him or whether he might be kept until July 1.

As Sweeney said, when asked if there was the possibility of keeping Eriksson for the remainder of the season without an extension, “Absolutely. Loui is a valuable player. Other teams are probably seeing it accordingly, as such. To me, he’s an impactful player on our hockey club. We value him. We’ve offered him a significant contract. There’s a gap there. That exists sometimes with players. We’ll see where it goes.’’

Trade talks, though, also have been ongoing. But, Sweeney pointed out the Bruins would need to find a commensurate player to replace Eriksson, if he were to be dealt, whether in that trade or elsewhere.

“My preference has been all along to try and sign him and go from there,’’ said Sweeney.

Poor timing

It was not exactly good timing. Zac Rinaldo already had been put on waivers earlier Sunday — to provide roster flexibility, Sweeney said — when, at 10:49 of the first period, he earned a check-to-the-head penalty on Cedric Paquette.

It was a hit that could earn him supplemental discipline. The Department of Player Safety was reviewing the play after the game.

History plays a significant role in supplemental discipline, with the possibility that a borderline hit rises to the level of a suspension due to what’s happened in the past. That could play a factor for Rinaldo.

“I think it was the right call,’’ coach Claude Julien said of the penalty, calling it “certainly warranted.’’

“The shoulder hit the head. So that’s part of what you’ve got to do here in this league,’’ he said. “We can criticize some of the calls tonight, but that one there I thought was right.’’

The Bruins acquired Rinaldo last summer from the Flyers for a 2017 third-round draft choice. He has played in 52 games, scoring one goal and two assists while earning 83 penalty minutes playing on the team’s fourth line.

A Connolly fan

It’s been a year since Brett Connolly was moved from Tampa Bay to Boston at the trade deadline. And, while he has his current charges to worry about, Lightning coach Jon Cooper has continued to keep tabs on Connolly.

The right wing wasn’t able to find the correct spot with the Lightning, but he has spent most of the season — nearly 60 percent of his shifts, according to Left Wing Lock — playing alongside Marchand and Patrice Bergeron on the Bruins’ top line.

“It’s been no secret, I’m a Brett Connolly fan,’’ Cooper said. “I just like what he’s done. He’s had some pretty serious injuries, when he played junior, and he’s kind of found his way from being kind of tabbed just as a scorer to now he’s refined his game. We don’t get to see him as often anymore, but you see him out there with two pretty darn good players — that means he’s doing something right because you don’t hand that ice time out for charity.

“So I’m really happy for how he has built himself into a regular NHLer. Just because it wasn’t quite the fit for us, it doesn’t mean he can’t be a fit somewhere else. You cheer for guys like that because he’s worked hard.’’

Making room The Bruins placed Max Talbot on waivers Saturday, which he cleared Sunday. The Bruins placed Rinaldo on waivers Sunday. Sweeney said those moves represented flexibility for the team. As for Rinaldo, Sweeney said, “I still believe that Zac is a player that we needed, the type of player that we needed. Did I know that Tyler Randell would be able to come in and fill a gap? Did I think Landon Ferraro, necessarily, would come in and fill another gap? No. Those are things you don’t necessarily have a great feel for before the season starts. I felt that our team lacked energy at times last year. I think that Zac has done a really good job in that regard. Has he produced at a level maybe he’s capable, when you watch him in practice every day? No, he’d probably be the first to tell you that. But I think his game has certainly come a long way.’’ . . . Asked about what he would like to find on the trade market, Sweeney said, “I think the overall depth of the hockey club is something we want to continue to identify and try and improve. Most of the talks have centered around draft picks; a lot of prospects have not changed hands.’’

Amalie Benjamin can be reached at abenjamin@globe.com. Follow her on Twitter @amaliebenjamin.