The 25-year-old has been in outstanding form this season and his performance against Barcelona - which included a spectacular double save from Neymar and Alexis Sanchez - further bolstered his bid to take the England No 1 jersey from Joe Hart.
Forster's rise to prominence has sparked interest from Spanish champions Barca, while Manchester United and AC Milan have also been linked with a January bid.
Despite Forster playing an integral role at Parkhead, Lawwell insists Celtic will not be holding him back should a bigger stage beckon.
"These things sort themselves out," he told the Daily Record.
"If we're bringing players here to develop them and get in the Champions League and they do well, England is down the road.
"If we are offered the right fee, we will take it and reinvest in another keeper or another centre forward or another midfielder."
With both Premier League and European clubs keeping tabs on Forster, Lawwell is the first to admit Celtic will not be able to compete with the salaries on offer.
"Also within that equation, if a player is trebling or quadrupling his wages, then it's an easy decision for him," he said.
"So there's no real friction preventing that happening. The player is happy, the club, for the right fee, is happy and the buying club are happy.
"No matter what we do, there is a realisation that in a very short period of time, the next-door market can pay huge amounts of money that we could never compete with."