The 24-year old striker is out of contract in 18 months but is attracting plenty of interest from Premier League clubs and Lawwell wants to secure his signature to a new long-term contract.
"Ideally, we'd like to see a conclusion to the talks with Gary," he said.
"Neil (Lennon) wants him to stay, we want him to stay. He has been a revelation and Gary has the last 16 of the Champions League to keep him here.
"We'd hope to hold on to him in January. We'd hope to hold on to all our players in January and get into the last eight because the manager wants it and that's what we will try and do.
"Is it risky letting a player enter the last year of contract? That's the balance. We need to try and get value out of Gary. But hopefully he will re-sign."