Rodgers is among those rumoured to be shortlisted for the Arsenal vacancy, after Arsene Wenger announced he would be leaving the Emirates at the end of this campaign.
However, Celtic's squad are a little reluctant to let go of the man who could well guide them to back-to-back trebles this season. Although the club will not impede discussions with Rodgers, Forrest was adamant they want him to remain.
He said: ''Since he has come in he has given us all confidence and made sure we've all been working hard and that's what we've done. I think we've done really well since he came in winning trophies, winning cups and we want to keep progressing and hopefully we can keep doing that.''
Forrest added: ''He's done a great job himself, he's getting linked to big clubs and that's only a good thing for Celtic and him personally. Obviously the players and everyone associated with the club wants him to stay and we hope that happens.''
If Celtic can defeat their rivals, Rangers, on Sunday, they will claim the Scottish Premiership title, and Forrest wants to see the club secure the league without delay.
He said: ''We just take it a game at a time, we want to make sure we tie up the league as quickly as we can now and obviously look forward to the cup final. There is always pressure at Celtic in every game. There's pressure to win trophies, to win cups and it is always going to be the case."