The 24-year-old only made 17 appearances for the Scottish champions last season after injuries and other off-the-field problems, but his manager wants to keep hold of him
The Republic of Ireland international has scored 31 times for the Hoops in 80 SPL appearances, but managed just seven goals and 17 appearances last season through injury and off-the-field problems.
However, after seeing Stokes set up two goals and named man of the match in the Scottish Cup final win over Hibernian, Lennon believes the 24-year-old still has a big future with the club.
"His record is good," Lennon told the Sunday Mail. "Twenty plus in his first two seasons, and then I think he got seven in 12 starts when he came back after January.
"He rejected our initial offer but I would imagine we'll come again and get him done.
"I'd like him to stay and I don't really think he wants to go, so we'll speak to his agent over the next week or so.”
Stokes missed most of Celtic's 2012-2013 Champions League campaign through injury, but their qualification for next season’s competition means he will get another chance in European football.
"I think the injury, and sitting out the Champions League games sparked something in him,” added Lennon.
"Can I trust him at European level? I think so, yeah. I think he's coming to that age when he's maturing and physically he's getting stronger.
"He's been around long enough to know what's expected of him now and I think he'll play more of a part in the bigger games.
"He's a great lad - he just lets himself down. He has that self-destruct button at times but more and more, he's tending to shy away from that now."