The Teessiders are working on the formalities of a short-term deal for the 34-year-old former England midfielder, who was released by QPR earlier this season, and hope to have him available to boost their bid for promotion from the npower Championship as early as this weekend.
Mowbray told the club's official website: "It's a deal that suits both parties. Kieron and his advisors have been very, very honourable in the discussions.
"I'm happy he's here. He's a good lad and a good pro. He wants to play football and he's happy to be here - hopefully he can contribute and help us succeed."
Mowbray knows the former Newcastle player well from their time together at Ipswich, and he is confident he still has something to offer.
He said: "I've known Kieron a long time and coached him for a year or two at Ipswich before he moved on. At such a young age, he was a fabulous footballer and he's still a fabulous footballer.
"Obviously he's had injury problems for a lot of years. People keep throwing statistics at me of how many games he's played and for how long, but I look at his record of where he has played this year.
"I watched him play against Manchester United this season and against Gareth Bale at Tottenham, and he was fine. We will have to see how he handles the intensity required in this league."