Club captain McManus, who has been at the club since he was a youth, was a favourite under old boss Gordon Strachan.
But the 27-year-old has failed to keep his place in the side under Mowbray this term, and looks set to join Willo Flood, Chris Killen and Barry Robson on Teesside.
Tony Mowbray: "I am not resigned to losing Stephen.
"I think it is an opportunity for him.
"I will put on record what a fantastic man he is and what a fantastic player he has been for this club and if this deal doesn't happen he will be back on the training ground and striving to get himself in the team.
"He is a great leader of men and they are in shortage but this is an opportunity for him and something that he is exploring and we will wait and see what develops."