Ex-England hooker George Chuter looks increasingly likely to leave Leicester when his deal runs out in the summer.
The 36-year-old, who joined the club in 2000, recently said he has had no talks about extending his contract and has been linked with a move to Sale.
Cockerill has not ruled out a new deal but hinted that this season could be Chuter's last for Tigers.
"George has a lot of experience and will offer a lot to somebody," Cockerill told BBC Radio Leicester.
"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.
"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 after making his debut in 2006 and is the Premiership's all-time top appearance maker with 259, as of 13 February.
But with the emergence of current England hooker Tom Youngs at Welford Road, Chuter is not first choice for Tigers and has only started three league games this season.
Cockerill added: "There are clubs that will look at his experience. George has done a very good job for us, not only this year and through his whole time at the club.
"We are looking at our options at hooker because I think that is the right thing to do. Chutes' may or may not stay and we'll have to wait and see, but we'll manage it properly.
"I know George very well and we are having those discussions all the time. At this point there are lot of decisions to be made."