The Daily Record says Lennon tried to land the striker, then at Everton, on a six-month loan deal in January 2011 but missed out because of an administrative error.
Now the manager - who is desperate to recruit extra firepower after watching his side score only three goals in six pre-season games - will try again to sign the former England Under-21 frontman who is poised to quit Norwich.
A source said: "An offer to go to Celtic would be too good for James to turn down.
"He was excited about the prospect first time and was disappointed when it didn't happen.
"Also, the chance to get involved in European football would appeal.
"I don't think he would be difficult to deal with if the opportunity arose to join one of the biggest clubs in the world."