Green led a consortium which bought Rangers' assets in May 2012 and then raised £22m from a share issue, but resigned from his post last year.
He returned for a short-lived spell as a consultant before selling his shareholding in the club.
However, he has spent the last week in talks with potential investors.
Rangers plan to launch a new share issue in a bid to raise in the region of £8m and if Green is to be successful he would need to convince existing shareholders to sell to a new consortium.
Green, who held the same position at Sheffield United, stood down from the chief executive's position citing the "negative publicity" surrounding an independent investigation, commissioned by the club's board, into allegations of undeclared dealings with former owner Craig Whyte.
That investigation consequently found no evidence of Whyte's claims that he was involved in the Green-led acquisition of Rangers two years ago.
On selling his shares to Sandy Easdale, chairman of Rangers' football board, in August 2013, Green said: "I want to make it clear that this means I will have no ongoing influence or financial interest at the club but I remain a fan and fervently hope that Rangers will soon be back at the top where they belong."
The Ibrox board met institutional investors in London last week, with the new issue to take place before the end of August.
Current Rangers chief executive, Graham Wallace, recently told fans that the Ibrox club was "in a good place" financially.
But, according to the BBC a minimum of £7m is needed to cover a cash shortfall at the newly-promoted Scottish Championship outfit.
Major shareholders Laxey Partners and Sandy Easdale, chairman of the football board, have both indicated they will buy more shares.
The Union of Fans - a collective of Rangers supporters groups - has urged people to withhold season-ticket money in protest against the board's running of the club.
It led to question marks over the ability of the club to meet the sales figures required for next season.
However, Wallace insisted Rangers are "in a good place" despite concerns over the club's finances.
The chairman's 120-day business review set out the club's intention to raise fresh equity in the autumn, win promotion from the Championship at the first attempt next season, before adding a Scottish title and being competitive in Europe by 2017.
The club's interim accounts revealed losses of £3.5m for the six months to 31 December and "going concern" status was only granted on the basis of predicted rises in season-ticket prices and sales.
The board have had to seek emergency funding in recent months.
Rangers declined to comment on the proposed new share issue.