Versatile back Goneva, 31, who is out of contract in the summer, has scored four tries in nine games this season.
He has 35 tries in 80 matches in total for Tigers since 2012 and won the 2014 Players' Player of the Year at the Rugby Players' Association awards.
"He is getting to an age where he is looking to move on," said Cockerill.
Wings Adam Thompstone, Telusa Veainu and centre Matt Smith agreed new deals earlier this week, and South African JP Pietersen was announced as a new addition to the squad for next season.
"We have to make sure that we get the balance of the squad right," Cockerill told BBC Radio Leicester.
"I don't know who keeps signing all these backs, but we have to get the balance right and have some forwards as well."
Cockerill added that finding a suitable replacement at hooker for Toulouse-bound Italy international Leonardo Ghuraldini was a priority, and they are also looking for an experienced prop.
"We need to make sure that hooker position is right, with experience and depth," Cockerill said.
"We are a senior prop short, maybe. We need to see how that settles with guys like Matias Aguero and those young lads coming through and whether they are ready to step up and be part of the senior squad on a more full-time basis."
Fiji international Vereniki Goneva may leave Leicester Tigers at the end of the season, according to director of rugby Richard Cockerill.