Chairman Alastair Johnston has told BBC Scotland that the independent committee of the Rangers board is closer to approving Craig Whyte's takeover bid.
Only last week Johnston put forward an alternative proposal, initiated by his fellow director Paul Murray.
But a meeting between the committee and Whyte on Sunday evening has helped persuade the sceptics.
"The committee are now much closer to viewing Craig Whyte's bid as the right one for Rangers," said Johnston.
A source close to Whyte also told BBC Scotland: "We're very optimistic a deal can be done if Alastair Johnston and the committee are minded to back it.
"It's very good news and all parties will proceed to try to bring this to a conclusion as quickly as possible."
There are still one or two minor details to be ironed out with Lloyds Bank, who currently handle the club's debt, but Whyte now appears to be on the verge of taking over from majority shareholder Sir David Murray.