Calderwood, who has won two of his 14 games in charge, has been unable to add to his squad so far in the January transfer window and Thornhill's capture would represent his first signing as boss.
He told HibernianTV: "We're very hopeful Matt Thornhill from Nottingham Forest will join us shortly. We have concluded a deal with the player and the club - subject to him being able to prove his fitness.
"It is not a long-term injury but he has missed two or three weeks of training. He is a midfielder who has a record of scoring goals and I think that makes him a good addition to any team and to any squad.
"He is a simple footballer, very unfussy, but he gets the job done."