Douglas Arneil, technical administrator for schools and youth at the SRU, will ask schools if they want to participate in "some form of competitive structure".
Any structure is likely to be similar to the existing youth leagues operated by the SRU. If there is sufficient interest, the league could begin in the 1997-98 season.
The game hopes the move will boost interest among players, teachers and parents and the wider public and raise playing standards.
The initiative comes at a time when a survey conducted by the department of public health sciences at Edinburgh University suggests that schools rugby is not as dangerous as previously thought.
A comparative study between players from nine Edinburgh schools and 26 senior SRU clubs in the Borders in 1993-94 showed that the prevalence of schoolboy match injuries was 86.8 per 1,000 to 367 per 1,000 in the senior game.
Professor Michael Garraway said: "Schools rugby is safer than has previously been reported and than I had suspected before we started."
He added: "The game in general is taught very well in school in terms of skills and techniques."