Lennon watched the 23-year-old in international action for Finland against Slovenia in midweek and remains hopeful of adding the striker to his squad in the coming days. Schalke have already turned down one offer for the player they signed from HJK Helsinki two years ago but Lennon is confident that, with Pukki not a regular pick for the Bundesliga side, a deal could be concluded soon.
"We have put a bid in and Schalke have said they're not willing to sell," revealed the Celtic manager. "But these are the barriers you come up against now and again. We do like him, we think he's a very intelligent player who can make us better so we're still negotiating.
"He's similar to Gary. He's got that stocky build. He's maybe not as physical as Gary but his movement is excellent and so is his first touch. He's a good finisher. I think he'll suit our style of play. I've seen him in the flesh now a couple of times. He's an impressive player but he's not getting much football at Schalke which might work in our benefit. [I saw on Wednesday] just how good his touch is and he's a team player. A lot of things Finland did went through him. He created a couple of decent opportunities for himself and this is international - not club level - we're talking about. He came out of it pretty impressively."
Celtic set off for Kazakhstan immediately following this afternoon's league match with Aberdeen at Pittodrie to give themselves more time to recover and prepare for their Champions League tie against Shakhtyor Karagandy on Tuesday.
Lennon can register one wildcard signing with UEFA ahead of Monday's deadline but didn't expect Pukki to make the journey even if a deal could be concluded before then. "No, we'd be basically looking at the second leg," he added. "We'd have no time to get the visa done. We'll be all hands to the pump to get him in - or we do have other options as well."
Lennon poured cold water on the suggestion that goalkeeper Fraser Forster could be moving to Benfica. "It's a rumour that's spread in the last few days. I don't know if they're trying to unsettle the player. There has been no concrete enquiry for him. There's no way I'd let him go."
The Celtic manager also expressed his disappointment at the news that the Next Gen series of European youth football was being suspended for a season due to a lack of funding. Lennon revealed he would now put more of his youth players out on loan to gain greater experience. He said: "It's disappointing to see that because I always feel that it's good for them to play against their peers from different countries at club level."