And the keeper also backed his old boss at Cardiff, Malky Mackay, to be a success if he is given the green light to take over the Parkhead hot seat.
The Scotland No.1 is in the perfect position, given his connection with both men.
And he admits he was disappointed when Mackay was removed from his position at the Welsh club earlier this season after leading them to the Barclays Premier League.
Marshall was also surprised when last week Lennon - who has been strongly linked with the soon-to-be vacated Southampton job - called time on his four years in charge of Celtic.
The race to succeed him is hotting up, with Michael Laudrup and Morten Wieghorst now emerging as contenders to form a Danish duo at the helm of the club, while Owen Coyle is reported to have had a tentative conversation with the Hoops.
But Mackay remains one of the men at the head of the field, and Marshall - who has met up with Celtic stars Scott Brown, Charlie Mulgrew and Leigh Griffiths for tomorrow's friendly at Craven Cottage against Nigeria - can fully understand why.
He said: "It would be a good job for Malky.
"His stock is high with what he did for us at Cardiff. As an ex-Celtic player who has done well taking us to the Premier League, I think he must be up there in the running for it.
"It's a completely different job at Celtic, but he will know that, and that's something he has in his favour.
"He was at Celtic from a young age, so knows how big the club is, how big the job is, and how important it is.
"They start early with the qualifiers. And, with no Rangers in the league, the Champions League is massive for them.
"It is a hard season if they don't get there.
"If they went straight into the group stage, a lot of managers would take the job in a second.
"But, it's hard to get in there, and that shows how well Lenny has done."
Lennon has now stepped away from that particular challenge, and Marshall is sure he will resurface at a top club.
He said: "When you hear someone has left their position, you automatically think there must be another job there for them.
"But, it seems that's not the case. He will get a good job, because he has done really.
"The next job he picks will be big for him."