The SRU wants to be able to sell all, or part of, Pro12 clubs Glasgow Warriors and Edinburgh Rugby.
The union has called a special general meeting on 28 October when member clubs can vote on a rule change.
In a letter sent to member clubs, the union said it has to be "inventive and innovative".
If a two-thirds majority backs the motion, outside parties would be able to invest in or take ownership of Warriors and Edinburgh. The SRU currently owns and funds them both to the tune of around £5m per year each.
However, BBC Scotland has learned that the SRU would want to ensure buyers would make commitments in terms of future investment and in bringing through young Scottish players before selling stakes in either pro team.
The Scottish game's ruling body feels getting substantial outside investment is the only way its professional teams will be able to compete in years to come with teams in England's Premiership and France's Top 14, both of which have benefited from huge increases in money from television companies.
Scottish Rugby chief executive Mark Dodson told BBC Scotland last month that he would be prepared to talk to interested parties about giving up control of Glasgow and Edinburgh if the price was right.
In a letter to be sent to member clubs and obtained by the BBC, SRU President Rob Flockhart says: ''The history of rugby in Scotland is characterised by a willingness to make bold decisions; we have to be inventive and innovative as we seek new income streams that will enable us to safeguard our ongoing investment in the domestic game and still support our pro-clubs at an appropriate level.
"It is increasingly clear that we must look at all options in order to attract more external funding. Your president, board and council now all seek your support to proceed to help us look to secure further investment in our great sport."
The special general meeting is to take place on 28 October.
The Scottish Rugby Union is asking members to allow it to put the country's two professional teams up for sale.