Celtic have urged the SPFL to issue the fixture calendar for the new season “as soon as possible”.
The new Premiership season will start behind closed doors on the weekend of 1 August – if Scotland is in phase two of its coronavirus recovery.
Premiership clubs have been given a targeted return date of 11 June for player training before the new campaign.
Talks will continue regarding how lower league football will restart.
Sports minister Joe Fitzpatrick met the heads of the major sporting bodies on Friday to discuss restart plans.
Celtic chief executive Peter Lawwell, who contributed to the meeting, has welcomed the prospect of a phased return for training and competitive matches, in line with the safety of all concerned.
“The past few months have been extremely difficult for supporters, players, staff and clubs right across the game,” Lawwell said.
“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.
“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.”
Celtic were crowned Scottish Premiership champions, and Hearts relegated, when the SPFL agreed to call the season on 18 May.
Scottish football has been suspended since 13 March, with Friday’s meeting mapping out a potential return to action.
Celtic manager Neil Lennon said his squad will be ready to return as and when they are given the green light.
“Our work off the pitch never stops and since the suspension of football was announced, we have been ensuring that our players have all they need across all areas in terms of their physical condition and all other elements of their welfare,” he added.