Scottish Rugby has made a bid for Murrayfield to host a British and Irish Lions match before the South Africa tour in 2021.
It would be the first time a Lions team has ever played on Scottish soil.
The Welsh and Irish unions have also made bids to host the match against an as yet unnamed opponent, which would be a warm-up game before the squad flew.
The SRU wants to make the event a weekend festival of rugby at the end of June 2021.
Twickenham is set to be unavailable with the Premiership final due to take place there on Saturday, 26 June.