Celtic have called on the SPFL to publish next season’s fixture list “as soon as possible”.
Neil Doncaster, the league’s chief executive, announced on Friday that his “firm target” is to have the 2020-21 Premiership campaign kicking off behind closed doors on 1 August.
He was speaking after talks with Scotland's national clinical director Professor Jason Leitch and sports minister Joe FitzPatrick.
The Scottish game's Joint Response Group has recommended lifting the suspension of all football activity from 11 June, which would allow Premiership players to return to training in preparation for the new season.
The 1 August date is provisional and the Premiership season will only begin if Scotland is in phase two of its coronavirus recovery.
There has been speculation that matches between Celtic and Rangers would be held over until 2021 in the hope that they could be played in front of spectators.
Celtic said in a statement on Saturday: “We have been given a targeted return date for player training of June 11, 2020 with Scottish Premiership matches hoped to commence on August 1, 2020.
“Celtic has been working tirelessly to do all we can to assist in achieving a return to football and we would hope the SPFL are in a position as soon as possible, to issue the fixture calendar for the forthcoming season.”
Peter Lawwell, the Celtic chief executive, who contributed to Friday’s meeting, added: “Everyone at Celtic warmly welcomes the decision in principle to a phased return to training and matches, while fully accepting that all decisions made in this regard must continue to have the safety and well- being of all concerned at their core.
“The past few months have been extremely difficult for supporters, players, staff and clubs right across the game. While we accept there will be no immediate return to normality, we are moving in the right direction and we thank our fans for their patience, understanding and support during these unprecedented times.
“I would like to also thank all our medical, safety and operations staff at Celtic and those across football for the extensive work they have done in striving for a safe return for us all. Celtic has, for some time, been engaging with relevant experts in this field - knowledge and guidance which we have shared with the joint response group, other Scottish clubs and the Scottish Government in order to support a safe, effective and quick return to football.
“Clearly, the important work we have done will be crucial as we move forward. We need to get back to football, safely, as soon as possible. That is our message and that is our aim.
"Our supporters are everything to us and our focus, ultimately, will be to do all we can to bring our fans back to matches as soon as we can. Our promise is to work as hard as we can to get our fans back to Celtic Park, to liaise closely with Government and the footballing authorities to find solutions and return to normal as soon as possible.
"The majority of leagues across Europe are back training, some already playing and many already with agreements in place to bring supporters back to matches. We can assure our fans that this will also be Celtic’s priority.
"In the meantime, we thank our fans sincerely for their continued engagement with and support of the Club. While we are still celebrating our title win, hopefully we can now look forward to the return of our fantastic 9 in a row team in the near future and look ahead to more success on the field.”