The Light Blues board announced earlier this month that they were looking to raise the significant sum from existing shareholders.
But SportTimes understands that, having failed to generate enough interest from those who have already invested in Rangers, chief executive Graham Wallace has now turned to Ashley in a bid to plug the financial black hole at Ibrox.
Ashley already has a 4.56% shareholding in Rangers International Football Club plc and his SportsDirect company agreed a retail partnership with the club two years ago, a deal that was signed off by then chief executive Charles Green.
In March last year, Green announced that a naming rights agreement had been struck with SportsDirect, but the move - which was met with dismay by some supporters - was never completed.
Now, fans have voiced their concerns that Ibrox will eventually be branded with Ashley's company logo as the businessman closes in a significant six-figure investment.
A Union of Fans spokesman said: "Mr Ashley's initial purchase of shares in Rangers appears to have been linked to his Sports Direct merchandise deal.
"The only man inside Rangers who liked that deal, at the time it was put in place, was Charles Green.
"We hope that any possible assistance given to the board by Mr Ashley at this time will not see him clinch another favourable deal, perhaps to rename Ibrox at a knockdown price.
"Can the board confirm that renaming of Ibrox will not be part of any underwriting deal with Mr Ashley and that we will not be seeing garish Sports Direct signage defacing our iconic Main Stand?"
With Rangers' cash health once again being called into question, Wallace admitted last week that the £4million share issue is needed to provide 'financial support' this year, while chairman David Somers refused to rule out dialogue with potential saviour Dave King.
Loans to shareholder Sandy Easdale and lifelong Gers fan George Letham, worth a combined £1.5million, must be repaid by the end of the month.
The UoF spokesman said: "Why are the board persisting with these short-term, desperate measures?
"The club needs urgent, substantial investment - not a short-term fix which will be lucky to see us past Christmas.
"Even if they are successful in raising the £4million, almost half the money will immediately have to be used to repay overdue loans.
"The board indicated to us that they could raise this money 'at the push of a button'.
"Sandy Easdale also stated, pre AGM, that investors were lined up. Clearly, neither of these statements have turned out to be true.
"Also, the vast bulk of this money could have been raised by greatly increased season ticket sales if the board had been prepared to properly safeguard the club's assets."
Any deal for Ashley to significantly increase his stake in Rangers is likely to come under the scrutiny of the football authorities on both sides of the border, and at the highest level in Europe.
The businessman owns English giants Newcastle United and the UoF have raised fears over his potential conflict of interest between Ibrox and St James' Park.
The spokesman said: "We are also concerned that, under Uefa regulations on dual ownership of clubs, Mr Ashley cannot have a 'decisive influence over decision making' at Rangers without it leading to the possibility of us not being able to compete in European competition.
"He could find himself holding around 20% of the shares in our club, having control of all club merchandise and being the largest single shareholder if he underwrites this share issue.
"Will the board clear this unequivocally, and in advance, with Uefa, to ensure that Rangers will not miss out on European football in the future because of Mr Ashley's ownership of Newcastle United?"