The left-hander seeks his sixth win in eight starts when he faces the Cleveland Indians in the final game before the All-Star break Sunday.
With the White Sox (45-50) in fourth place in the AL Central, Danks (8-6, 4.15 ERA) could be moved before the July 31 trade deadline. Going 5-2 with a 2.85 ERA in his last nine starts has only increased his value.
"It's just something we'll have to deal with if it comes, but like I said, that's the furthest thing from my mind," Danks told MLB's official website earlier this month. "I feel like I'm somewhat coming into my own, and I'm trying to ride it out as long as we can. But yeah, I feel great right now and I'm happy to be contributing here."
The left-hander wasn't at his sharpest Tuesday in Boston but got enough support for an 8-3 victory. He gave up three runs and eight hits over 5 2-3 innings, and matched a season high with four walks.
He fared even worse at Cleveland (46-47) on May 2, giving up eight runs and 10 hits in five innings of a 12-5 loss. Danks had gone 3-1 with a 2.79 ERA in his six previous starts at Progressive Field.
He's 1-2 with a 10.20 ERA in his last three overall matchups with the Indians, though he allowed three runs over six innings of a 7-3 home win April 10.
He might not have Alexei Ramirez to help him in this start, as the All-Star shortstop exited in the fourth inning of Saturday's 6-2 win because of a stiff back.
Fellow All-Star Jose Abreu hit his major league-best 29th homer and Gordon Beckham had a two-run double as the White Sox ended a three-game skid. Beckham, also a subject of trade rumors, was 1 for 30 in his previous seven games and was benched in a 7-4 loss in Friday's series opener.
The Indians will try to bounce back with their eighth win in 12 games this month and 12th in 15 home matchups with the White Sox. Chicago has won five of the past six overall meetings.
The White Sox also gave Trevor Bauer one of the most difficult outings of his career in his lone matchup June 28, 2013. Bauer (3-4, 4.23) was charged with five runs while recording two outs but avoided the loss when Cleveland rallied for a 19-10 victory.
The right-hander had a much better showing against the New York Yankees on Tuesday, outdueling Masahiro Tanaka. He allowed three runs in the first two innings but gave up one hit and no walks in five ensuing innings in a 5-3 victory, his first in four outings.
Outfielder Chris Dickerson is uncertain to play after missing Saturday's contest with a tight left hamstring, though manager Terry Francona indicated it wasn't serious.
Dickerson has gone 8 for 17 in five games since being acquired from Pittsburgh after Michael Bourn suffered a hamstring injury.
"He's done a really good job. He's been on base a ton," Francona told MLB's official website. "When a guy goes down and somebody fills in and gets hot, it really helps."
White Sox outfielder Adam Eaton, dealing with a jammed left wrist and a sore right ankle, likely won't play Sunday.