The Hoops boss is intent on getting his business done by July 2, when the bulk of his squad will return for pre-season training.
Lennon wants to have the new men bedded in long before their opening Champions League qualifier on July 31.
He is convinced he already has the nucleus of a team which is only going to improve.
But Lennon – who has already secured central defender Jaroslaw Fojut on a Bosman – wants to augment what he has, preferably with some experience.
To make room for them he is ready to trim some of the surplus which has accumulated around his squad. The likes of Glenn Loovens, Daniel Majstorovic, Mark Wilson, Cha Du-Ri and Darren O'Dea are coming to the end of their contracts and head the list of players expected to be freed.
Lennon revealed: "Some of the players have been told already, but not all of them."
Asked if he was talking in terms of half a dozen players, Lennon confirmed: "There will be roughly around that mark. The squad is a little bigger than we want and, hopefully, we will be trimming it.
"We want to add three or four quality players to that, and we don't want to clog up the young ones coming through, as well.
"We want to give them the opportunity to play in the first team and see if they can bed down a regular place."
While reducing the wage bill is essential to make room for new arrivals, Lennon also wants to raise more spending money by selling. He has not ruled out the possibility it could be one of his established players who goes, though he is intent on retaining in-demand striker Gary Hooper.
But if a substantial offer for the likes of Ki Sung Yueng was forthcoming in this window, the manager and the Celtic board could face a big decision.
He said: "We'd like to have players in by July 2, when we start pre-season, so we can bed them in as quickly as possible, and that's what we are working on.
"I don't know if we are in the marquee market and, looking at the squad, I don't know we need to be because they are all blossoming nicely.
"If you bring that one superstar in, it might tip the balance of the squad."