Glaswegian Davies has enjoyed success at the City Ground, saving the Reds from relegation last season and transforming them into Championship promotion contenders in his first full campaign at the helm.
Forest are guaranteed a play-off spot but Davies has made clear his frustrations regarding the club's complex transfer policy.
Interim manager Neil Lennon's hopes of landing the Celtic job on a permanent basis could have been fatally damaged by the embarrassing Scottish Cup defeat to Ross County, although he has overseen four successive league wins.
Davies, who also guided Preston and Derby to the Championship play-offs and took the Rams all the way to the top flight, was a candidate to replace Gary Megson at Bolton before Owen Coyle took that job in January.
On this latest speculation, the 45-year-old said: "My only focus is on finishing the job this season. The only thing I am thinking about is my job at Nottingham Forest. I want to get this club through the play-off semi-finals, to Wembley and hopefully back into the Premier League. That is the only thing I am thinking about."