However, Davies was quick to refute any claim he was in contact about the post.
Davies said: "I've got a job to do at this football club and the one thing I will not do is show disrespect to the manager who currently sits in that position.
"I've got my own situation to take care of here, which is to take this football club moving forward and apart from that nothing else matters to me.
"Do I view it as a compliment? I've been linked with jobs in the past and they're always lies and it is just mischief making."
Jamie Paterson had fired Forest into the lead just two minutes into the second half.
But Matt Mills directed in Andre Moritz's cross with 15 minutes left on the clock to make sure Bolton took a point.
Davies was happy that his side kept their unbeaten run going, with the result extending it to nine games, but signified that he needs to strengthen.
Davies added: "It was a frantic game of football that could have gone either way.
"Defensively today we were excellent and the only thing that we are lacking is that clinical finishing up front.
"What I've done is pass my names on to the club and we agreed that this was a plan and what you need to do at this time of the year is strengthen to kick on."
- Sports & Recreation
- Sam Allardyce