Leigertwood is available on a free transfer after seeing out his contract at Reading earlier this summer.
A number of clubs have shown an interest in Leigertwood, but Forest are thought to be leading the chase for the 31-year-old.
Leigertwood missed a large chunk of last season with an ankle injury, but returned to action at the back end of the campaign and he is fit and raring to go as he seeks a new club.
Forest boss Stuart Pearce is believed to be in the market for a defensive midfielder and he has identified Leigertwood as his top target.
Leigertwood has a wealth of experience having played in the Premier League for Crystal Palace, Sheffield United and Reading and Pearce feels he could be prove to be a key component to his squad for next season as he looks to mount a bid for promotion.