According to BBC Sport, the SRU has received offers of investment from 11 different groups, but only four of those were realistic proposals.
Of the serious contenders, one is interested in taking a stake in the Borders, one in Glasgow and the other two say they would take any club.
SRU chief executive Gordon McKie said: "We are very hopeful that an investor can be found."
But he admitted that they could yet face a difficult decision by their self-imposed deadline of July.
Scotland's governing body had been looking at ways to stem a £23m core debt, leaving a question mark over the future of at least one of Edinburgh Gunners, Glasgow Warriors and Border Reivers.
"No decision has been made about which side could go, but it's unlikely to be Edinburgh because of the number of Scotland internationals who play for them," said McKie.
The SRU is hoping to franchise out at least one of the teams that play in the Celtic League and European competitons.
"Our budget requirement is £1m, but we would be happy to accept two minority stakes of, for example, £500,000 each," said McKie.
"Equally, if someone came along and said they were willing to give us £1.5m if we gave them control then the answer to that would be 'possibly', subject to legal advice.
"So we are amenable to any proposal in which somebody wants to own and drive a pro-team while we become a silent partner."
The SRU has set itself a deadline of the end of June to find an investor but are prepared to explore fresh avenues in an effort to keep three teams in existence.
"Option one would be to look into our budget to see if we can find the money to cover the cost there," said McKie.
"Option two would be to make one of the teams a development side, while option three would be to lose one of the teams."
The SRU chief is desperate to see all three teams invested in for the future but conceded the finance may not be achieved soon.
"It is conceivable that, in time, we will go down this path with more than one team and my view, and the board's view, is that might be no bad thing," added McKie.
"But it would be impossible to have all three pro-teams receiving outside investment in the timescale available to us.
"If we can get outside investment into one team by the end of June then that would be a good result, not because of scarcity of candidates but just because of the logistics of what is involved."