It is understood that Scotland, Wales and Ireland are all possible hosts for a potential Lions fixture against a so far unnamed opponent.
The game, if it takes place, would be in late June 2021 ahead of departure to South Africa for an eight-match tour that features three Tests against the world champion Springboks.
Twickenham, meanwhile, is unlikely to be available as the 2021 Gallagher Premiership final is scheduled there for June 26.
“We are always open for business, and have a track record of putting on big events beyond Scotland Test matches, such as football games for Celtic, Hearts and Liverpool, music concerts and European and Guinness PRO14 rugby finals,” the Scottish Rugby Union said in a statement to the PA news agency.
“We have as rich a Lions history as any of the nations, and it would be great to host the famous red jerseys on Scottish soil for the first time.”
And they tackled the Barbarians in Hong Kong eight years later, prior to touring Australia.
Sign up to our mailing list for a weekly digest from the wide world of rugby.Sign Up Now