Reports suggested that Davies had been considered to take the reins at Upton Park after his side humiliated Sam Allardyce's side 5-0 in the FA Cup third round.
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."
Bolton manager Dougie Freedman was pleased with his team's performance but was not happy with the amount of time wasting.
He said: "I'm delighted from the response of the players after the way that they were set back in the second half.
"But I wasn't happy because we created enough opportunities in the first half to take the lead.
"In the second half we made a very good Nottingham Forest side look ragged towards the end of the game. That's a great credit to our players for the way they showed that and with our possession and opportunities we created we should have taken the win.
"I thought the referee managed the game very well but I was disappointed for both sets of fans for how much time wasting that wasn't stamped down on."
Speaking about adding to his squad, Freedman added: "We're down to the bare bones at the back, so that's where we are looking to strengthen in January.
"But I'm not just going to throw money at it, we've got to do what's right by this football club."