Edinburgh and Glasgow Warriors players have been invited to return to training on 22 June, Scottish Rugby chief executive Mark Dodson has confirmed.
If the Scottish government's route map out of lockdown moves from phase one to two on 18 June, players will be given the option to resume fitness work.
All professional players in Scotland are currently on the government furlough scheme.
Both squads will be based at Murrayfield.
Dodson said the players had been "invited to voluntary fitness sessions, making sure that we keep players fit for a presumed return to contact rugby at the end of August, early September".
The Pro14 is expected to return on 22 August with a series of derby matches. That would involve Edinburgh and Glasgow meeting at Murrayfield behind closed doors, possibly for a double-header on consecutive weekends.
'Presumption autumn Tests will be behind closed doors'
The future of the international game is far more uncertain. Scotland's summer tour to South Africa and New Zealand was cancelled as a result of the coronavirus pandemic. The All Blacks, Argentina and Japan are scheduled to visit Murrayfield in November.
Matchday revenue accounts for a huge chunk of Scottish Rugby's income, so even if the autumn internationals go ahead, the prospect of playing them behind closed doors presents a financial problem for the union.
"The issue around the autumn Tests is crucial to us," Dodson said. "The reason everyone is talking about social distancing from 2m/1.5m/1m to zero is that it has a significant impact on how many tickets we can sell, how many people can come through the door and enjoy whatever Test schedule we can put forward.
"From where we stand at the moment, our presumption is that those Tests will go ahead behind closed doors until we're told different from government."
The salary and bonuses awarded to Dodson and other Scottish Rugby executives in recent times has been fiercely criticised, and the chief executive says the business operation is "under review" amid the coronavirus pandemic.
"We are looking at all methods to deal with this," he said. "We're modelling every impact on the business and looking across the sport and entertainment spectrums."
Dodson also confirmed talks have taken place with Hearts and Hibernian about the capital clubs using Murrayfield as a 'bio-bubble' when football returns, though stressed those talks were at an early stage.
Discussions around a new global rugby calendar, which would align the seasons of northern and southern hemisphere rugby, have been taking place throughout the shutdown brought about by the pandemic.
And Dodson added: "We're very happy with summer rugby. We think it's good for participation at grassroots level. The most crucial thing about this is the global alignment not only releases revenue opportunities, is that it works for everyone.
"From where I sit there's more co-operation than ever before and people are looking to make sure the emerging nations are catered for."