In-coming Celtic chief executive Dominic McKay will not be allowed to make his move to Parkhead early after Murrayfield bosses insisted he see out his notice period.
McKay is due to replace Peter Lawwell on 1 July but many in the Hoops support believe the change needs to be made now following Lennon's resignation and the collapse of their 10-in-a-row dream.
However, Scottish Rugby Union chief executive Mark Dodson is adamant McKay - who currently serves as his number two - will be going nowhere until they find a new man for his chief operating officer role.
"What's happening at Celtic is out of my control," said Dodson. "It's not something I'm utterly familiar with but I do know Dom is going to have a very full in-tray when he gets there.
"The issue for us is that he has a notice period that he has to serve here and we need stability in our business too.
"So I expect Dom to be here with us for a while."
Dodson added: "We're going though a restructure process here anyway so Dom moving to Celtic just gives us a chance once more to look at what we're going to do.
"But yeah the roles will be replaced and we'll make sure that we take or time and get some outstanding candidates to replace Dom."