Leadbitter has been a prime summer transfer target for Forest boss Billy Davies and has already been the subject of several failed approaches.
However, with less than a week to go until the transfer window closes, Forest are refusing to give up on their pursuit of the 27-year-old.
The midfielder has started all five games for Boro this season and manager Tony Mowbray expressed his belief last month that Leadbitter wants to stay at The Riverside.
Mowbray said in the Evening 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 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."