Murrayfield, in Edinburgh, hosted World Cup games in 2007
Scotland are in discussions with the three other home nations about co-hosting the 2015 Rugby World Cup.
And SRU chief executive Gordon McKie has thrown his weight behind a joint bid from the four home nations to host the 2015 and 2019 events.
The Scots, along with England, Ireland and Wales, have indicated their interest in being hosts in 2015.
"We believe that a four home unions bid would make a compelling proposition for world rugby," said McKee.
England, Ireland, Scotland and Wales, were among a record eight countries to indicate their interest to the International Rugby Board for 2015.
Italy, South Africa, Australia and Japan have also confirmed they will tender for the 2015 event.
Over the coming months, we will be conducting a detailed evaluation of what's involved in hosting or co-hosting RWC 2015 and/or 2019
Scottish Rugby chief executive Gordon McKie
Russia joined the same countries, with the exception of England, in expressing interest in the 2019 tournament.
The bidders have until May to decide whether to make a single bid or make it jointly with another nation or nations.
"Scottish Rugby is committed to ensuring that any decision it makes in respect of hosting RWC2015 and/or RWC 2019 is in the best interest of growing the game and leaving a lasting legacy for the sport in Scotland," said McKie.
"We've been encouraged by the support to date which is being shown by the Scottish government and other public sector partners and, over the coming months, we will be conducting a detailed evaluation of what's involved in hosting or co-hosting RWC 2015 and/or 2019."
Scotland has been a venue World Cup games previously, in 1991, 1999 and 2007, when the official hosts were England, Wales and France respectively.
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But the final itself has yet to be played at Murrayfield.
A spokesman for the IRB, which will announce the winning bids for both the 2015 and 2019 tournaments in July, said: "The IRB has no stated preference on joint bids or sole bids.
"We will judge each bid on its merits."
The next tournament will be held in New Zealand in 2011.
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