The SFA president hopes Premiership chiefs and broadcasters agree to postpone games for the sake of the national team.
Steve Clarke’s side are two matches away from qualifying for next year’s European Championships.
Scotland face two games in four days next March — with Petrie hopeful players will be given the weekend off beforehand.
He said: “There is a degree of cohesion and understanding between the SFA and the league.
“Clubs understand that the more successful the national team is, the more revenue comes into the association to funnel back to them. It is a win-win situation for them.
“Everyone is desperate to get back to a finals. The prospect of Euro 2020 and Glasgow hosting four games is something that spurs us on.”
It’s understood the SPFL believe it will be difficult to organise any shutdown.
But Petrie will bide his time before making any proposal.
He said: “There is a right time to ask any question. You shouldn’t ask it too early, you shouldn’t ask it too late.
“We are not at that time yet for March 2020. Broadcasters haven’t made their picks for that part of the campaign.
“But once we finish this campaign we will take a look at the play-offs.”
Clarke could take his players on a week’s training camp if league games were postponed.
Petrie said: “Right now it is about getting ourselves well prepared.
“If there is something like a camp, then I am very open to having those conversations.”
Meanwhile, Petrie has revealed the SFA are pushing ahead with plans to be part of a joint UK bid to host the 2030 World Cup.
The plans, which could see Hampden redeveloped, are at an advanced stage.
Petrie said: “We are in discussions with other home associations.
“The bid gives us a ten-year timeline to look at Hampden as a host for World Cup games.”
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