Leadbitter has reportedly attracted interest from Nottingham Forest during the close season, with Boro rejecting a pair of bids for the midfielder.
Mowbray believes that Leadbitter is excited about forming a midfield partnership with Dean Whitehead this season, dismissing claims that the 27-year-old is open to leaving Boro.
He told the Middlesbrough Gazette: "The positive for me on Grant is that he's said to me many times he enjoys being at Middlesbrough FC.
"He enjoys the training, he enjoys coming to work every day and I am very confident in my own mind that he's not looking to move on. He's very settled and looking forward to the season. He was very important to us last season and he will be moving forward with us I'm pretty sure.
"He's happy with Dean Whitehead's arrival at the club, somebody he knows well, and in training they've been bouncing off each other. They are both very competitive and it's brought an edge to training. And we're looking forward to the midfield being a strong department this season."
Leadbitter made 47 appearances for Boro last season in his first campaign with the club, scoring four times.