The 28-year-old Scotland international striker has not played for the Hoops since December 8 due to personal issues, as reported by The Scottish Sun.
The former Wolverhampton Wanderers striker has been training recently, and Celtic manager Lennon has suggested that he could be available for the Scottish Cup final against Hearts.
Lennon told The Scottish Sun: “What have we got until the Cup final, six weeks? Yeah. It’s realistic.
“But he’ll have to play and train at least two weeks going into that, so he then has a target of four weeks.
"He’s had targets. He’s working away in the background and doing his double sessions.
“He’s getting there. It’s a slow burner, but we understand that as he’s been out for such a long period of time.”
Griffiths is one of the best strikers in Scotland, and Celtic could have done much better with him in the squad over the past few months.
The Scotland international could take a while to get back to his best, but if he plays competitive football in the final weeks of the campaign, then with a strong pre-season, then he could play a major role in the Champions League qualifiers.