While the Hibs boss didn’t make it clear how much the club are demanding for the player, he simply stated that Celtic’s offer fell short of their requirement.
Celtic are quite interested in signing the 23-year-old, who has a year remaining on his Easter Road contract.
“We have rejected two bids from Celtic,” said Lennon, as quoted by Sky Sports.
“Our club has a valuation of the player. I don’t know what that is, but obviously Celtic have not met the valuation that Hibs want.”
Hibs already rejected an opening £1.5 million for the Scottish midfielder, and according to Sky Sports, a second offer around £1.75 million has also been rejected.
McGinn, capped nine times at the senior level for Scotland, is a very good midfielder and was superb for Hibs last season.
Celtic boss Brendan Rodgers has earmarked the 23-year-old as one of his key summer targets after the Bhoys lost Stuart Armstrong to Southampton this summer.
Hibs will face NSI Runavik in the Europa League qualifier and Lennon believes that McGinn will be in the right frame of mind to play the game.
“He’s been all right,” Lennon added. Obviously it is difficult. Listen, I have been a player myself, so it’s difficult dealing with speculation.
“Obviously when a club as big as Celtic come in for you there is always that anticipation, from his point of view, of maybe making that step forward, if you want to call it that.
“However, he has to be professional. We have had a couple of chats over the piece about it. He will just have to wait and see how it develops because he is our player, and he’s a very important player for us.”