Marshall, who has just joined Hull City from Cardiff City, is in line to start Sunday's World Cup qualifier in Malta.
The 31-year-old played in nine of Scotland's 10 Euro 2016 qualifiers and their two end-of-season friendlies.
"For me, David is the number one and he should remain the number one," said Rough, who won 53 Scotland caps.
"I'm a great believer when you are number one, unless you do something wrong, you should remain number one.
"It doesn't matter how good the other two are even if they are playing out of their skin; if you are holding that position, you should stay there until you do something wrong.
"In the last campaign, I would say David Marshall was our star man. He has the ability to make the international saves - and the important saves when it's really tight.
"I think he's matured beyond anything you would have imagined."
Marshall's move to Premier League Hull, after 280 games in seven years at Cardiff, could affect the long-term future of McGregor.
The 34-year-old is currently sidelined until probably the new year following back surgery and may struggle to regain his place following the arrival of his Scotland rival.
"It's not a good problem if you are the goalkeeper that's number two," said Rough, who suffered a similar fate when Andy Goram joined Hibs and relieved him of his first-choice status towards the end of his career.
"That's when you've got to make decisions - 'do I want to be here?'. I'm sure Allan would have to look at that situation depending on how long it went on.
"It is a massive problem, but a manager will tell you it's a good problem.
"I'm sure the two of them will work together. But the longer you are number two then you've got to start making decisions."
Craig Gordon, who is in the current Scotland squad preparing to face Malta, has found himself relegated to the bench at Celtic.
The 33-year-old played in their first nine games this season, but new signing Dorus de Vries was handed the jersey for last Saturday's Premiership match against Aberdeen.
Rough believes Gordon will reclaim first-choice status, but not for next week's Old Firm encounter against Rangers.
"I still think Craig is good enough and has the ability to fight himself back in there," said Rough, 64.
"But the manager has to select De Vries against Rangers. He's picked him to play in the previous match. It would just throw out confusion to everybody if he didn't.
"Fortunately, he's been given a fortnight to get used to the back four that will play in front of him. But I think that is what has been the problem - not Craig's problem - but Celtic's problem; they haven't had a settled back four, not even a settled two central defenders.
"I think Craig's problem is he's been trying to cover for the people in front of him and on the odd occasion he's been found out.
"Craig's biggest problem is the standard he set when he joined Celtic - he was unbelievable. It's very difficult to maintain that kind of level.
"He's got to accept that's he's been dropped, not for the wee small error, because everybody loses these kind of goals; he's been dropped because the manager said this guy [De Vries] is better with the ball at his feet. But I think Craig will get back in."
David Marshall deserves to be first-choice goalkeeper for Scotland despite the claims of Allan McGregor and Craig Gordon, believes ex-keeper Alan Rough.