(CBS) The White Sox’s chances of moving All-Star reliever Jesse Crain took a dip Thursday after the right-hander said his right shoulder didn’t feel better.

Crain, who hasn’t pitched in a game since June 29, played catch from about 100 feet Wednesday, but said he felt he’d still need to rest his shoulder. He had hoped to return to the mound Sunday, but that now seems unlikely.

“I’d rather be throwing in the pen and wasn’t up to it today,” Crain said. “So it’s still a process, day by day. Hopefully it starts to feel better.”

Several contending teams, including the Braves, are reportedly interested in acquiring the 32-year-old reliever before the non-waiver trade deadline on July 31.

“Obviously, I wanted to be getting better and I obviously wanted to be able to pitch, the most important thing,” Crain said. “It’s always discouraging when you work hard to get back, and it’s not responding.’’

Pitching coach Don Cooper said the team will just have to be patient with Crain.

“The first thing on our mind is to keep him healthy,” Cooper said. “It’s disappointing for him and for us not to have him. That’s a big hole on our team in that seventh and eighth inning in the role he was filling so well. He just needs more time. It didn’t happen today.”