But the Hoops boss admits it is every bit as important that the club holds on to the quality they already have.
With 10 days to go until the window closes, Holmbert Fridjonsson and Stefan Johansen are the only new arrivals. But, while everything is being thrown at concluding deals which Celtic have been working on for several weeks, Lennon concedes vital housework also requires their full attention.
Negotiations have already begun with Georgios Samaras and Joe Ledley. With their current deals six months from completion, neither man has yet been persuaded to commit to a new contract.
Chief executive Peter Lawwell is sure to be involved in more discussions, but the indications are the experienced pair will still be at the club when the window closes.
And, when asked what was more important, new additions or keeping what he already has in his squad, Lennon replied honestly: "It's both. It would be nice to keep Joe and Sami, if we could, and obviously look at strengthening the squad in the areas we want to.
"That is exactly what we are going to try and do."
The Hoops have been linked with several players since the window opened three weeks ago, most recently £6million-rated attacking midfielders, Norwich's Robert Snodgrass and Benfica's Filip Djuricic.
Celtic have also been included in the list of clubs tracking Middlesbrough defender, Rhys Williams. But, securing a proven goalscorer remains the No.1 priority for Lennon.
Leigh Griffiths has indicated he would be delighted to be given the chance to prove he is the man to finally fill the boots of Gary Hooper.
But, Celtic have yet to take the Scotland striker up on his offer.
His present club, Wolves, insist there has been no contact from the Scottish champions.
And Molineux boss, Kenny Jackett, does not anticipate he wil be getting a call any time soon.
He said: "If the phone rings, we'll see. But it's not something I'm going to worry about. He's not someone we have transfer-listed or are actively trying to sell, and it's all hypothetical unless anyone comes in."
Jackett added: "It's interesting to hear Leigh's comments on Celtic. They are a big club and, as a Scotland international, that will be of some interest."
Despite his come-and-get-me plea, Griffiths has not requested a transfer, and Jackett continued: "His attitude has been fine. He's had no problems, caused us any problems, or expressed any desire to leave. It's the first I've heard of it.
"At present, he's in a group working towards beating Bristol City on Saturday. That's our focus and, if there is an offer for anyone, we'll deal with it."
Meanwhile, the agent of 17-year-old Hungarian striker, Mark Murai, has claimed his boy has been invited to Celtic for a trial.
Balint Kovacs said: "We've asked permission from his club, Koposvar, to travel, and they have allowed him."