Chief executive Mark Dodson will unveil the proposal at the union's annual general meeting next Saturday, 5 August, BBC Scotland has learned.
The SRU would invest at least £100,000 annually in each of the teams for the first five years, a total of over £3m.
They will contest a six-team semi-pro league, with play-offs to follow.
There is likely to be one team based in Glasgow, one in Edinburgh, one in the Borders and one in the North and Midlands district, with two others elsewhere.
It is hoped the new set-up, which follows a comprehensive review of the whole club structure of Scottish rugby, will be up and running for the start of the 2018-19 season.
The fully professional teams, Glasgow Warriors and Edinburgh Rugby, would remain in their current guises.
Underneath the semi-pro league, there would be an amateur national league of four divisions each containing 12 clubs.
The BT Premiership, the top tier of the Scottish club game, has 10 clubs at present, with the National One, Two and Three leagues featuring 12 clubs each.
Some clubs have yet to be convinced of the plan.
One club representative told BBC Scotland: "I doubt we have enough good players to make it work and it might cost more to set up than the union envisages."
The strategy will be presented at next Saturday's AGM to the clubs, who will then have time to consider the proposals, although there is no plan for a vote of the member clubs.
Scottish Rugby owns and funds both of its two professional teams, Glasgow and Edinburgh, to the tune of about £5m per year, although is open to outside investment in both.
Scottish Rugby is planning to create six semi-professional franchise clubs as part of a radical restructuring of the game in Scotland.