The plan is to charge a £1 levy on tickets for concerts at the venue to help fund the music industry.
The cash raised would fund grassroots music and arts programmes, with a figure of around £1m estimated.
Hampden and Murrayfield would be the two stadiums included, as the big outdoor arenas that attract the biggest acts.
Next year P!ink and Foo Fighters are among the global acts to play Hampden.
Calvin Harris and Red Hot Chilli Peppers played the stadium this year with Beyonce and Ed Sheeran taking tot he stage last year.
Green MSP Mark Ruskell has backed the call from the Music Venue Trust for the levy.
He asked Culture Minister Angus Robertson and wants the Government to bring forward the proposal.
Ruskell said: “The Music Venue Trust illustrated how just £1 from every ticket sale at gigs in Scotland’s two largest stadiums would generate a million pounds a year.
“This summer we have P!nk and the Foo Fighters lined up for sold-out gigs at Hampden in Glasgow and Taylor Swift coming to Murrayfield in Edinburgh to name just three. “Think what difference that could make if this was in place.
“These are examples of how the profits of big culture could be reinvested into grassroots music, artists and cultural venues.”
Ruskell said the culture minister told him he would look at the proposal but said the backing needed must come from the music fans, who buy the tickets.
He added: “They are the driving force that attract big-name acts to our towns and our cities with their buying power.
“It is their loyalty and enthusiasm that signals demand, and it is that same community who can help make a difference.
“I would urge them to get behind the campaign and demonstrate the strength of feeling that exists in ensuring we examine all new ways to help fund culture, including a badly needed stadium tax.”
“Scotland’s arts sector and venues help bind the very fabric of our society, from the jobs they deliver to the dreams they inspire and we should look at every single opportunity we can to protect and support it however we possibly can.”