Edinburgh will miss the services of Fiji back-row Bill Mata for the next eight weeks after suffering an ankle injury.
The 28-year-old sustained the injury during Edinburgh's Challenge Cup quarter-final defeat against Bordeaux and will now miss the opening phase of the new season for the Scottish regional club and also the Autumn Nations Cup when Fiji will come to Europe.
"Bill Mata will have surgery on his ankle on Thursday to repair a ligament," said Cockerill.
“He will probably be six to eight weeks with that, meaning he will miss the first two rounds of the PRO14 with us then the international period with Fiji.
“Once he has surgery we’ll know more, it may be shorter, it may be longer but roughly it will be six to eight weeks.
“It’s tough. He has been playing very well. We know Bill is pivotal to ourselves so it’s disappointing.
“We’ve got good cover with Nick Haining and Magnus Bradbury. They are good number eights so we’re not short in the back-row but certainly for Edinburgh and Fiji that will be a blow.”
Edinburgh will face Ospreys in the opening round of the 2020/21 season of Pro14 at BT Murrayfield Stadium on Sunday.