Speaking in Dublin yesterday to publicise the inanely-named Dublin Decider (only a person who hates sport, probably some marketing-type chappie with a pink shirt and a ponytail could come up with a title like that for a pre-season friendly which will decide nothing at all), a game between Celtic and Liverpool at Lansdowne Road on August 10, Lennon had a number of names thrown at him as possible transfer targets.
Many Irish players are likely to be on the move this summer: senior internationals such as Richard Dunne, Keith Fahey and Stephen Hunt are certain to leave their clubs and others, such as Kevin Doyle, Sean St Ledger, Stephen Ward and Shay Given, are in need of a move, so Celtic will be seen as a possible destination.
Lennon admitted his admiration for Doyle and Dunne, though confessing that the latter's age (the defender will be 34 later this year) could count against any deal, but Glasgow could be a magnet for players, including some of Giovanni Trapattoni's squad.
As things stand, Anthony Stokes – due to sign a new deal with Celtic as his present one has run out – is the only Republic of Ireland player likely to be near the group stages of the Champions League next season, and Lennon feels that the lure of Europe could be a factor.
"With what we achieved last season there is more of an incentive for players to come to Celtic," he said.
"The Scottish football environment isn't the most attractive for a lot of people and I know the economics are difficult, but if you are coming for money and football, then football-wise there is no better place to play.
"The likes of Chris Sutton, Alan Thompson, Stiliyan Petrov all left. Even Craig Bellamy said this week, when you leave then something leaves with you, there's not the same edge to it that Celtic can provide, not just in terms of winning silverware but that edge to your life and the atmosphere to the place.
"It's a hard environment to prosper in but when you do it gives you a real sense of satisfaction and pride," he added.
"The Irish connection is very important. Myself and Mr (Dermot, majority shareholder) Desmond are very strong on that, to have a bond running through the club with an Irish theme. We like to have Irish players at the club.
"Not just because they are good enough but they understand the history of the club, I think that's very important."
So Kevin Doyle could be a target, as the striker clearly needs to leave Wolves to rescue his career, something that Lennon feels could be done at Parkhead.
"I have always admired Kevin as a player. In January I was looking to bring another striker in, he fitted the bill. He was having a bit of a tough time of it at Wolves and we felt that coming to Celtic would re-energise him again and give him that zest for football," Lennon said.
"You don't lose the talent but it is mentalit. Confidence goes a little bit or you're in an unhappy place, and we felt that coming to Celtic would have given Kevin that spark again.
"He has definitely got it and towards the end of the season he started to bang in a few goals for Wolves. Whether we go for him again, we will talk about that, we will decide later on."
Sean St Ledger is a regular at Parkhead as a fan and, as the defender is unwanted at Leicester City, he could also interest Celtic.
"Sean is a good player, he played very well against England and showed his qualities. He's not a name that's been on our list but he may do. You can throw names at me and I don't like talking about business in public. Sean has been on the club's radar for a while," Lennon said.
"We are well aware of Richard Dunne and Richard is a tremendous player. His age might count against him in terms of us but I would not rule anything out."
The club had one senior Republic of Ireland player in the side last season and while talks between Celtic and Stokes over a new deal have yet to be completed, Lennon hopes the Dubliner signs a new contract.
"We have offered him a new contract, negotiations are ongoing, but I am pretty confident he will be here with us next year," Lennon explained.
"With the injury he had, he missed out on the Champions League campaign and I think that hurt him. He is one of those lads who doesn't get injured that often – it was a pre-season game against Inter Milan where he hurt his ankle and he didn't realise how bad it was until a week or two after.
"So he had the surgery and the four-five months he was out made him realise what an opportunity he had.
"He is actually a good athlete. With his physical stance and the work that the sports science team have done with him he is right up there with anyone in terms of running power and natural body strength.
"He has taken all that on board and, to be fair to him, he looks in great condition. He had a great end to the season. He has always had the talent, over two seasons he scored 20-plus goals for us which is a godsend and he's an important player to me."
Lennon knows that non-Irish names will also be linked with his club, while they will also face a battle to hold onto their own top-rated players like Victor Wanyama and Gary Hooper.
"It's the silly season for us in Scotland, particularly at Celtic or any of the other big clubs, you get names thrown at you all the time," he said.
"I was at the French Cup final last Friday and the next day in the paper I was linked with about seven French players.
"We haven't made a concrete decision on any player yet and have had no bids.
"We had good income this year from the Champions League money so we may have a bit more to spend than in recent years.
"There will be bids coming in for our players and we can't stop that. If we feel it's good business for the club, then we will reinvest the money like we did with the money we got for Aiden (McGeady)."