The Hoops wrapped up their second trophy of the season with a 3-0 win over Hibernian in the William Hill Scottish Cup final.
The Clydesdale Bank Premier League champions also enjoyed a memorable year in Europe in which they beat Barcelona on their way to the Champions League last 16. And now the Parkhead manager is hoping to confirm a meeting with Irish businessman Desmond and the club's chief executive Peter Lawwell.
As well as discussing his own transfer targets, a decision will have to be made on the future of striker Gary Hooper.
The Englishman grabbed a brace against Hibs to take his tally to 31 for the season but the likes of Norwich, who failed with a £7million bid in January, are likely to move again for the 25-year-old.
Lennon told the Scottish Sun: "I'm due to meet Dermot and Peter, I'm going to sit down with them over the next week or so. I might even go to Ireland to see Dermot or see him in London.
"I'm hoping we can talk about what we're going to do for the close season because we haven't really had that conversation yet in terms of bringing players in, targets and what the budget's going to be.
"There will be a few players leaving and then I'm sure we'll get offers for a player or two.
"Sometimes you can't do anything about that. It depends on the offer if it's right for the club, if it gives us something we can build on, if you can replace the player that will go.
"There are some players I'd dearly love to keep and I'll be making that clear to Peter and Dermot."