07/25/2013 15:23 EDT | Updated 09/24/2013 05:12 EDT

White Sox reliever Jesse Crain off July trade block

Chicago White Sox general manager Rick Hahn has one less trade chip to play with leading up to the July 31 non-waiver trade deadline.

Toronto-born relief pitcher Jesse Crain had what pitching coach Don Cooper called a “slight setback” Thursday morning in his recovery from a strained shoulder and won’t be activated from the 15-day disabled list before the deadline.

Crain’s bullpen session was cancelled after he reportedly played catch and was forced to stop.

On Tuesday, the right-hander felt “OK” after throwing 33 pitches, a mix of fastballs and changeups, off a mound in his first legitimate test since last appearing in a game June 29.

Crain, 32, said he didn’t throw to his maximum ability on Tuesday because he wanted to use it as a gauge to see how he felt following the layoff.

Crain made the American League all-star team with a 0.74 first-half earned-run average but obviously didn’t participate.

He admitted to thinking of a potential trade “but right now I’m focused on being healthy and being able to pitch.”

Should Crain return soon, he would have to go through the waiver process before Chicago could trade him.

And Hahn wouldn’t have the chance to create a bidding war as he would only be negotiating with the team that wins a claim on Crain.

Starting pitcher Jake Peavy, outfielder Alex Rios and shortstop Alexei Ramirez are other White Sox that could be traded before August.