Celtic are looking for a new manager to replace Ronny Deila.
Monk and Rodgers worked with each other at Swansea City earlier in their respective careers, and still remain friends.
And Monk feels that Rodgers would be keen on taking the job at Parkhead, after Sky Sports reported that the former Liverpool boss was edging closer to landing the Bhoys’ job.
“I haven’t spoken to Brendan for a while, but he’s keen to get back into management and that’s an option for him,” Monk said.
“It’s a massive club. I’m sure that would appeal to Brendan.”
Rodgers is reportedly Celtic’s first choice to take over from Ronny Deila, as they look to move forward.
Deila has delivered two Scottish Premiership titles in his two seasons in charge, but the Bhoys’ lack of success in Europe has frustrated.
Rodgers’ appointment would be a signal of intent from Celtic, but whether the Northern Irish boss would be willing to take the job remains to be seen.
Rodgers has been out of work since he was sacked by Liverpool towards the end 2015.
Neil Lennon and Michael O’Neill are amongst the other managers to be linked with the Celtic job.