Scottish Rugby chief operating officer Dominic McKay says Murrayfield could help grow Scottish football’s audience.
The rugby body is to make a presentation to the Scottish FA proposing the stadium as a venue for football internationals and cup games.
Hearts are currently using Murrayfield, which hosts Scotland and Edinburgh rugby matches, for home games while Tynecastle is being redeveloped.
“We think we’ve got a very special stadium,” McKay told BBC Scotland.
“We’ve been given the opportunity by our friends at the SFA to put our best foot forward and bid for major events and those major events include Scottish international games but they also include cup finals and semi-finals.
“Largest venue in Scotland, 67,000 – it’s got outstanding transport links, it’s got outstanding broadcast and media facilities and importantly it’s got the space and the flexibility around the stadium to put on a very special match day.
“If we can help the SFA in the longer-term get more people to watch Scotland games then we’re up for that by hosting here at Murrayfield.”
Hampden, in Glasgow’s south side, will continue to host Scotland football internationals and cup semi-finals and finals until 2020.
As well as Hearts games, Murrayfield has also hosted Celtic European matches in 2014 while Celtic Park was being used for the Glasgow Commonwealth Games.
Hampden, first used for football internationals in 1906, hosted athletics during the Games and during its redevelopment back to a football ground, Ibrox and Celtic Park were used to host Scotland matches.
Scottish League One side Queen’s Park play their home games at Hampden, which has a capacity of more than 51,000. The ground will also be one of the 13 venues for Euro 2020.
“I think what we’ve found is when we’ve taken games outwith Edinburgh, when we take our Scotland games up to Aberdeen and over to Kilmarnock and into Glasgow, it’s helped to actually grow our audience,” McKay said.
“We’ve recently hosted the European Cup final of rugby, which was a huge success.
“We host major rock acts and music acts and of course we’ve had Celtic here playing their Champions League games. So hosting football’s not something that’s unusual for us. It comes naturally.
“And, importantly, we never need to forget that because you’re the Scotland national rugby team, our fans are travelling from a long way so sometimes we can make it easier for them to travel by moving the games closer to them. That’s quite a positive.
“It probably offers the opportunity for the Scottish FA to drive more revenue, to make more money than ever before, to reinvest back into football.”