The 36-year-old has been with the Tigers since 2000, but with his contract due to expire at the end of the campaign, it appears likely that he will seek pastures new.
"George has a lot of experience and will offer a lot to somebody. Whether that is us in the short term, or the opportunity is there to go somewhere for longer and potentially coach and do all those other things - he has to weigh those options up himself," Cockerill told BBC Sport.
"But the way guys leave this club is important to us and however that is managed, it needs to be done right."
Chuter won 24 international caps for England.