The 6ft 7in lock is set to miss Saturday's Premiership clash with London Irish, but Cockerill fears Parling's absence could roll on for some time.
"You would like to think that with the right rest and expertise he will be fine, but I don't know," said Cockerill.
"He's doing the usual cog-sport protocols and everything else they do.
"We will take some advice on that from people who know what they're talking about. He may need some down-time for obvious reasons
"It's a concern for his health. Playing is secondary."