Rangers International Football Club has rejected a possible £18m takeover offer from American Robert Sarver, saying it undervalues the Ibrox outfit.
But the board has invited the owner of the Phoenix Suns basketball outfit to invest in the Scottish Championship club along with other shareholders.
The news comes the day after football chairman Sandy Easdale loaned the club £500,000 to avoid a winding-up order.
RIFC admits that it will require further funding by the end of January.
"The directors are in discussions with Rangers' significant stakeholders with a view to arranging finance for the club," said a statement to the Stock Exchange.
"This is likely to comprise loans in the short term and possibly equity in the medium term.
"The board has invited Mr Sarver to consider participating in a similar discussion alongside other supportive shareholders."
Sarver, a 53-year-old banker by profession, purchased a majority ownership in the Phoenix Suns' National Basketball Association franchise in 2004 and also owns the Phoenix Mercury women's basketball club.
Rangers revealed that his plan for the Glasgow club involved buying 100 million shares at 18p per share - below the current share price of 26p.
"While the directors welcome Mr Sarver's approach, they believe that, notwithstanding the current financial difficulties, the proposal does not adequately value a controlling interest in the company," said the RIFC statement.
"And, accordingly, the resolution to approve the placing is unlikely to achieve the 75% majority required.
"The directors do not intend to hold the general meeting, which would be necessary to implement the proposal."
Sarver made his approach in December, but the news only broke in the media on Sunday and it was followed by Rangers appointing Sports Direct executive Barry Leach as their finance director.
Leach heads brands at Mike Ashley's sport retail business, the Newcastle United owner's associate, Derek Llambias, having already been installed as chief executive following Ashley's £2m loan to the Scottish Championship club.
In a separate Stock Exchange statement, Sarver stressed that his approach for Rangers was a serious one.
"First and foremost, I believe what the club needs today is a very quick, major injection of capital to stabilise things and I can give the Rangers supporters a categorical assurance that I have the resources and ability to get this club back to its elite level," he said.
"I'm looking forward to building a consensus amongst supporters and prominent Rangers-minded figures who have the long-term success of the club at heart.
"I've had detailed research carried out on Rangers and I'm convinced that we could take it back to the top of the Scottish game on a stable and sustainable basis."
Sarver also explained that his interest was ignited by a conversation with former Rangers defender David Robertson, who is now based in Arizona.
"My three sons all play soccer, as we call it here in the US, for Davie's club," he said.
"Initially, I'd had some of my advisors examining potential investments in teams in the English Premier League and in Spain, but Davie encouraged me to take a close look at Rangers."
Robertson, who played 245 times for Rangers over six seasons and was part of the side that won nine titles in a row, added: "I can tell every Rangers fan in Scotland and abroad, if Robert Sarver is successful in becoming part of the club, he'll not rest until they are back on top again."