According to the Daily Express, the Atonement actor leads a list of candidates to play the title role in the J.R.R. Tolkien adaptation.
A source is quoted as saying: "A number of names have privately been doing the rounds, including Daniel Radcliffe and Jack Black, but James is the one the film's bosses really want.
"They're expected to have talks with him soon so hopefully it could be confirmed in the not too distant future."
The Hobbit director Guillermo del Toro recently told Empire that he and producer Peter Jackson were closing in on an actor for the role.
Del Toro said: "I can tell you it's down to a few names that we all agree upon. For our first choice, completely magically, we all said the same name."
The role of Bilbo Baggins was played by Sir Ian Holm in the Lord Of The Rings franchise, but requires a younger actor for the prequel films.