The Parkhead manager toyed with the idea of leaving on a high after taking his team to the last 16 in the Champions League and winning a league and Scottish Cup double.
Lennon quickly decided there was more he could achieve, though. In an interview with Sky Sports, he said he would meet Celtic's majority owner, Dermot Desmond, and chief executive Peter Lawwell next week when an improved contract may be on the agenda.
"We talk about the contract situation every year," said Lennon. "I'll be meeting Peter, my chief executive, and Mr Desmond next week. Things now suit both parties - it has done throughout the last four years - but we'll sit down when the time comes, which will be in the next few weeks."
When he was asked if he was tempted to leave on a high last summer, a few months after a famous Champions League group stage win over Barcelona, Lennon said: "Yes. At the minute you're thinking 'is the last 16 the glass ceiling for a Scottish club?' But you come back and think 'can we do it again?'
"I think our strategy of bringing players in and selling them on is short-term, I think that'll change over the next three or four years.
"We'll be in a strong position to challenge again and that's a huge incentive to take the club forward. In terms of my own future I'm very lucky to be here."
Lennon also said came close to quitting during a campaign of intimidation in which he was sent bullets and letter bombs.
"I came very close to it, yeah, when the devices which were sent to me turned out to be viable ones. I thought about my family and my kids."
Lennon confirmed that he will rest some of his top players in the final seven games of the season, with more than a nod to Emilio Izaguirre and Nigeria defender Efe Ambrose who will be at the World Cup in Brazil, while goalkeeper Fraser Forster remains hopeful of finding a place in Roy Hodgson's England squad.