BOSTON — The White Sox dropped another underachieving starter Monday, designating Odrisamer Despaigne for assignment to make room for Jon Jay.

Despaigne follows in the footsteps of Ervin Santana, who was released after three starts in April.

Coincidentally, both went 0-2 in their three starts, and both finished with a 9.45 ERA. The Sox did not pursue big name free agent starters in the offseason, and patchwork fixes like Santana and Despaigne haven’t worked out.

Manager Rick Renteria said Dylan Covey will get a rehab assignment at Triple-A Charlotte this week, but could not say if he would be called up.

“I think we’ve got to take it one day at a time and then we’ll determine what we’ll do as he’s continuing to recover and gets his outings under his belt,” Renteria said. “We don’t want him to go down. We want to make sure we take a measured approach to bringing him back.”

Manny Banuelos also is on the injured list, and Carlos Rodon is out for the season after Tommy John surgery. The Sox won’t call up top prospect Dylan Cease until they feel he’s ready.

They’ll have a bullpen day on Tuesday, Renteria said, and with an off-day Thursday they won’t need a fifth starter until Sunday against the Twins.

One name under consideration is left-hander Hector Santiago, who was released by the Mets and signed to a minor-league deal by the Sox.

Santiago is tentatively scheduled to start Tuesday for Charlotte, and already has had two stints in the Sox organization. He posted a 4.50 ERA last year, mostly in the Sox bullpen.

Catch-22: Zack Collins was back on the bench Monday with James McCann behind the plate and Jose Abreu at DH while Yonder Alonso was at first.

Collins came into Monday hitless in nine at-bats since homering in Texas on Friday, and Renteria is not going to play him regularly.

“I’m not going to give you the dates but he might be catching tomorrow,” Renteria said. “We’ll have opportunities to be behind the plate. We have a lot of guys in that DH slot but we want to give him some at-bats. He’s going to work very hard at first base.

“We’re going to try to make him a multiple position individual at the major league level and develop his catching ability.”