The Latics were reported earlier this week to have given the defender permission to talk to the Black Cats, but it now appears that Baines will not be moving to the north-east.
Boss Chris Hutchings told the club's official website: "Leighton is finally over his virus. He trained for the first time this summer yesterday (Tuesday) and he will be involved in some capacity tonight.
"He's been laid low with a virus for the last couple of weeks and has been restricted to light training.
"He was with the rest of the squad in Holland working directly with our physiotherapists, but now he's been given the all-clear to get involved in the heavy stuff.
"Leighton is a first-class pro and a first-class person and, despite all the speculation and rumour surrounding his future, he's remained professional throughout and as ever is a joy to work with.
"I've coached him since he first broke into the first-team as a young apprentice and taken great satisfaction in how he's developed as a player and an individual."