The 25-year-old has a pre-contract agreement with the Bhoys to move to Glasgow on a free transfer in the summer.
However, the former Preston and Notts County man hopes a deal can be done that sees him link up with the SPL giants this month.
"That would definitely suit me because my mind is at Celtic," Wilson told the Nottingham Post. "I would prefer to move to Scotland this month and get on with my career.
"Celtic are in a good position at the moment and I'd like to do my bit as the team tries to win the championship.
"They are a huge club and I can't wait to get started. This is a move I have wanted for a long time."