At the end of the current year, Lennon would have served five years at the club, and whatever happens, he will definitley be remembered as a Celtic legend.
Lennon knows there is a possibility that Celtic may not renew his contract for another year, but would obviously welcome the decision if they did.
He said, "If the club want to come to me in January and review it, then great, but, if not, I am quite happy to see things through to the end of the season.
"We've left it open, as was the plan at the start of the season when I signed the contract.
"We'd said then we'd have a year and maybe top it up if they are happy with me and I am happy at the club.
"If not, I might hang them up or I might move elsewhere, but that's the last scenario we're looking at at the minute."
To be remembered as a title-winning captain is a priority for the midfielder, and this is the way Lennon wants to be remembered.
"I want to be a winning captain and getting the title back is my priority this season. That's what I'd like to be remembered by as a captain," Lenny said.
"I've won things as a player and that's been fantastic personally and, for the team, the past five years have been pretty successful.
"Now, from the team point of view, you want to win again, but, as the captain, it's a bit personal for me. It's great being captain, but to be a winning captain would be even better."