Manager Neil Lennon admitted it would be difficult to keep his squad together following their run to the last 16 of the Champions League, after their European adventure ended with a 2-0 defeat by Juventus in Turin on Wednesday night.
The key players who are most expected to move on are versatile midfielder Victor Wanyama and striker Gary Hooper, who attracted several bids from Norwich in January and is approaching the final year of his contract.
But Lawwell is keen to ensure that Lennon can hit the ground running when Celtic's next Champions League campaign begins.
As such, he does not look like sanctioning widespread departures - and promised to provide adequate replacements for those that do leave.
Lawwell told Sky Sports News: "I think inevitably there will be one or two players that will probably want to move on.
"But stability is a very important thing in football so we would hope to get the balance right, to make sure that there is some quality coming in that may replace those that are going, but keeping a real balance in terms of stability and continuity going into, hopefully, the qualifiers next July."