The capital club will lose Duhan van der Merwe to the English Premiership side in the close season but Sutherland will not be following the winger south, according to the Edinburgh head coach.
“Rory is under contract until the end of next season and that’s it,” said Cockerill, responding to a weekend report.
“He won’t be released from his contract. He’s an Edinburgh player until his contract runs out and from an Edinburgh and Scotland point of view we’d like to keep him long-term. It is as simple as that really – there is no truth in that whatsoever.”
Sutherland is currently sidelined with a shoulder injury sustained in Scotland’s Six Nations win over France in Paris in March. Cockerill said he was making good progress but his hopes of selection for the Lions’ summer tour of South Africa were in the balance.
“If selected, it will be tight,” said the Edinburgh coach. The Lions squad will be named on Thursday.
“Rory’s rehab is going well. He’s out on the field doing lots of running and whatever he can at the gym to rehab that shoulder,” added Cockerill.
“He’s working hard and is very optimistic around him being fit sooner rather than later.
“We’ll have to see. Those discussions will be had with our medical team and if they are being shared with the Lions selectors then I don’t know that.”