Davies steered Forest to third place in the Championship but promotion hopes were dashed when they lost to Blackpool in the play-offs.
"As a professional football manager there is not a job that I would not consider," he told STV Sports Centre.
"If the terms and conditions were right, if the club structure was right and the right support mechanisms were in place then, as a professional football manager, only a fool would turn around and say no to any interest from any club."
Regarding a move to Parkhead, he added: "Until something official had happened well, you look at the situation then. I can't stop the speculation. I'm employed by Nottingham Forest for another two years.
"I have got conversations I have to have with the board regarding what lies ahead in the future but all other speculation is purely speculation.
"I've had no official contact from anybody about any other job. My job is to focus on the balls, bibs, disc and cones as they say.
"From my point of view I certainly would not turn my back on any potential interested party if they make it official to Forest, if they agree compensation, and they do what is necessary.
"Until that happens I turn a blind eye to it, it's just speculation and I look forward to the challenge I've got as manager of Nottingham Forest."