Rodgers has become a favourite in the running for the Arsenal head coach position, after Arsene Wenger announced that he will be stepping down at the end of this campaign.
Desmond said of the speculation surrounding Rodgers: ''I'm glad he's the favourite. He's an outstanding person. We wouldn't want him to leave but we won't force him to stay. Hopefully his love for the club and the set-up here will induce him to stay.''
He added: ''I don't think you can put handcuffs on anybody if they want to go to a club as good as Arsenal. It will be Brendan's decision and his decision only.''
Rodgers has enjoyed incredible success with Celtic, and is on track to make Scottish history by winning back-to-back Trebles this season.