The 31-year-old did not have his contract renewed at the Britannia Stadium despite making 30 appearances in all competitions last season.
He is now a free agent and Mowbray is hoping to swoop as he plans to add experience to his midfield.
Mowbray told The Evening Gazette: “I feel he could help solidify us out of possession.
“Can we do it? I think the boy has got options but he’s somebody we’ve talked to and we’ll see what develops over the next few weeks.”
Middlesbrough finished 16th in the Championship last term after a dreadful end to their season, in which they won just three of their last 19 matches.