Ronny Deila will step down as the Celtic manager at the end of the season.
Ronny Deila is in charge of Celtic at the moment, but the Norwegian will leave the Scottish Premiership giants at the end of the season.
Lennon is a former manager of the Bhoys and is very popular among the fans, and ex-Arsenal star Parlour believes that the former Northern Ireland international midfielder would be good for the club.
Parlour has also suggested that former Everton and Manchester United boss David Moyes would not be interested in the Celtic managerial job.
“I can see Neil Lennon,” said the former England international on the Alan Brazil Upfront podcast on Audioboom. “He knows the club.”
“I think he (David Moyes) will bid his time, see what’s going to happen during the summer," added Parlour. "There’s always changes along the way, someone will move somewhere else and it will trigger managers’ merry-go-round."
Lennon was in charge of Celtic from 2010 to 2014 and was hugely successful as the club’s manager.
The former Nottingham Forest midfielder won the league title in the Scottish top flight three years in a row and the Scottish Cup twice.
With Lennon, Celtic will know what they are getting, and he is a ‘safer’ option than Moyes, who did well at Everton but struggled at United and Spanish club Real Sociedad.