The English striker, who has scored 28 goals this season, has been heavily linked with a summer move to Norwich City but Lennon is desperate to retain his services, especially after talking out a second straight Scottish title on the weekend.
"I have made my submission to the board regarding Gary. We will do what we can to keep him. I still think there is a chance he will stay," he said.
"Goalscorers are at a premium and he is only 24. He is one of those players who we feel is really settled here."