But the Hoops boss is confident the 24-year-old, who was Man of the Match in the Scottish Cup final victory over Hibernian, will stay at Celtic Park.
Lennon said: "We have already made him an offer - he has knocked that back, but negotiations will be ongoing.
"We really saw the best of him towards the end of the season. He looks physically in the best shape he has been in.
"He was such a pivotal player for us towards the end of the season, and his cup final performance was absolutely fantastic.
"The opportunity is there for him to go and make a good career for himself. He is very important to me."
Meanwhile, Lennon confirmed there has been no approach from any other clubs about any of his players, amid daily rumours in the media over the future of several Celtic players.
"There have been no approaches for any of our players at the minute," Lennon added. "It is what it is, the speculation, but we get that a lot.
"It's a back-handed compliment to what we have done with the players over the last two or three years that we have got so many young prized assets in the squad now."