The Scottish Sun says Wilson last night signed a pre-contract agreement to join Celtic in the summer.
And Hoops boss Neil Lennon hopes to sign Wilson this month and bring him to Celtic Park immediately.
Lennon said: "There may be some movement in the next few weeks. If not, then we'll have him in the summer. If the possibility is there for him to come here in January, then I'd like to have him now.
"It's up to Forest. They have their own priorities and he is still technically a Forest player.
"I played with him for six months when I was there. He was 22 and he was still developing physically.
"We have watched him the last couple of years and he's been very consistent in the Championship. He's very quick, composed on the ball and decent in the air as well.
"We did try and get him in August but there was nothing doing there."