The Easter Road boss revealed last week he had made the former Celtic striker a “strong offer” to return to Leith.
The Irishman helped Hibs win the Scottish Cup 15 months ago but since then his career has gone into a nose dive.
He signed for Blackburn last summer but has started just four games for Rovers, with his Ewood stint dogged by off-field issues before being released last week.
But his former Parkhead manager Lennon believes that with those personal problems now behind him, he can transform Stokes - who turns 29 on Tuesday - back into the feared frontman he was during his Celtic days.
“I’m trying to bring him in because I think he’s a good player,” said Lennon. “He’s won championships, he’s won cups and I think his best performances have come when he’s played in Scotland whether it be here, Falkirk or Celtic.
“So it’s an environment that he’s very comfortable in and can prosper in.
“I can’t comment on his personal issues but the majority of those issues are resolved and behind him now.
“It’s important that he gets back playing football. He’s 28-29 now. He has a bit to prove to people but I believe he has qualities that will enhance us.
“If we can get the deal done then great, if we can’t we move on.
“But I do think his best years came under me at Celtic so I think that will certainly work in my favour.”
Lennon is also keeping a slot in his squad free for another of his former Hoops stars Kris Commons.
The 33-year-old - who is currently recovering from back surgery - says he will only take up the option if he can regain the strength required to make a mark for Hibs.
But Lennon insists the ex-Scotland international is far from finished at the top level.
He said: “Kris is a very proud individual. He knows there’s an interest from us - but nothing more than that.
“He has to prove his fitness. He knows himself, it’s a back operation - it’s going to keep him out for a couple of months but it’s not career threatening.
“I still think he has plenty of football in him. When he came here last season he wasn’t fit but still scored two goals in five appearances. If he comes through the op okay and can get himself back up to full speed then he will be an asset to any club.
“But it will be Kris’ decision whether he signs ultimately.”
Meanwhile, Lennon confirmed Deivydas Matulevicius will miss Tuesday night’s Betfred Cup clash with Arbroath as Hibs are still waiting on international clearance from the Belgian FA following his move from Royal Mouscron.
However, his Lithuania team-mate Vykintas Slivka is due to complete a season-long loan from Juventus this week.