Lennon revealed talks between Celtic and Wolves were ongoing after the Sky Bet League One promotion hopefuls confirmed they had rejected an offer.
The former Livingston and Dundee striker scored 28 goals for Hibernian last season in his second loan spell with his boyhood club and has hit 13 goals for Wolves so far this term.
Lennon said: "He had a fantastic season last year. I think he has improved as a player and there is scope for him to get better.
"It's not just his goals: he can see a pass; his movement is very, very good; he has got physically stronger; he has got pace about him as well.
"He has broken into the Scotland squad. He knows the environment and I think he would improve here with the players around him."
Lennon brushed off suggestions that the attempted signing was unpopular with some Celtic fans, and questions over whether 23-year-old Griffiths could help them improve in the Champions League.
"People would have said when we brought Gary Hooper in that you hadn't heard of him," Lennon said. "You hadn't heard of (Victor) Wanyama and (Emilio) Izaguirre, people like that.
"People say 'he can't do this' and 'he can't do that'. They all did it.
"We believe that, if Leigh comes here, he can play at this level comfortably and, at his age, there is a good five, six years for him to improve and reach his peak.
"Scott McDonald came here from Motherwell a few years ago and scored a huge amount of goals and went on to score in Europe as well. I think Leigh can do the same."
Griffiths has made headlines off the pitch but Lennon is not put off.
"We all have issues away from football so I'm not going to touch on them because I don't know the ins and outs of them," he said.
"What I see is on the pitch. If there are difficulties then we will help him and manage him. But he's a good player and I think he will come here and make us better."
Celtic first of all have to persuade Wolves to part with a player who signed a new two-year contract in August with a further 12-month option.
Lennon said: "We have made our intentions clear and the talks will keep going now for however length of time it takes to get a resolution one way or another."
Griffiths has only started two of the last seven matches, since Wolves boss Kenny Jackett criticised his work-rate after taking him off at half-time in a defeat by MK Dons, and he did not come off the bench during a 3-1 win over Bristol City on Saturday.
And Jackett would not rule out selling Griffiths if a higher bid came in.
The Wolves boss told his club's official media team: "We do understand every player has their price but we are not desperate to sell players here.
"Leigh has gone public to say he is interested in the Celtic situation as most Scottish lads would be when a club of that size come in.
"But the deal would have to be right for us and they have made some initial contact that has been turned down. We will have to see how the week develops and whether that bid improves."
Lennon stated his club had no other bids in but he is hoping to do more business before Friday night's transfer deadline.
"We have other irons in the fire," he said. "We are hoping we can get some things done in the next couple of days."
That action could be influenced by the responses of midfielder Joe Ledley and forward Georgios Samaras to new contract offers.
Both are free agents in the summer and the club do not want them to depart for nothing.
Lennon is looking for answers from the pair this week and, when asked whether Friday's deadline will have any bearing on their futures, Lennon said: "Possibly, yes, and the players are aware of that as well."