The Scots-born star, who once had a trial at Ibrox, said his firm held discussions with a consortium about becoming a major investor after the club went into administration, before the consortium led by Charles Green took over.
Ramsay, 46, said: "We were talking to a consortium about the potential to take them into the Conference and then work our way over the next five or six years into the Championship in England, and from there to the Premier League.
"I didn't go public. It was something I was interested in but didn't want everyone to know about."
He added that, had he been successful, his friend David Beckham would not have been persuaded to pull on a blue jersey.