Forest are third in the Championship with just two games of the regular season left.
And the 45-year-old Scot, who was forced to suppress the rumours he would be moving to Parkhead, is instead focusing of the play-offs.
He told BBC Radio Nottingham: "The fact I've signed a contract tells you I want to be here. The fact that I have two years left tells you I have work to do. I've had a wonderful 18 months or so at Forest but the job is not done."
Neil Lennon is in temporary charge of Celtic following Tony Mowbray's departure, but Davies, who has another two years of his City Ground contract to see out, is the latest name to be linked with the post.
"The focus is on the remaining matches and getting the team to the Premier League," he added. "In the summer I will sit down and discuss with my advisors and representatives the way the situation is with regard to the future and we will look at the future and we'll make decisions."