Lawwell also said that discussions remain ongoing with English striker Gary Hooper and Kenya midfielder Victor Wanyama over new Parkhead contracts.
The Hoops confirmed Israel defender Rami Gershon's six-month loan deal from Standard Liege as their first finalised transfer deal of the January window.
Young Australian Central Coast Mariners midfielder Tom Rogic has also been handed a trial during the Scottish club's winter break in Marbella and more new recruits could be on the way as Celtic chase a domestic treble.
Lawwell, whose team face Italian champions Juventus in the last 16 of the Champions League next month, said: "We always like to strengthen. If the right opportunity comes along, we would like to do that.
"We would hopefully come out stronger than where we are at the moment. If they don't appear, then they don't appear.
"We have scouted a lot of players. January is not the best time to be doing it but, if we believe there is somebody out there, with the right deal to strengthen the squad and it's do-able, we would do it."
On first-team stars Hooper and Wanyama, Lawwell added: "We are continuing to talk until there is an offer for players that they want to take and go or they sign a contract.
"It would be wrong to put a time limit on it. We are in a good place as a club at the moment. Thankfully we've got a lot of talent.
"We've got players who will be sought after but we are managing that and we have a good track record of managing that in the past. There have been no offers for any of our players."