Ashley owns roughly 7% of the Glasgow club and it is believed that he has pledged to make a significant loan as they continue to suffer financial troubles.
A statement released this evening by Rangers supporters coalition The Union of Fans said: "It has come to our attention that the Rangers board are considering a move which could see Mike Ashley underwrite the £4m share issue they previously announced.
"This has been necessary due to understandably poor take up from existing investors. We believe the SFA have been approached to find out what would be required to give clearance for this, due to Mr Ashley's ownership of Newcastle United.
"We would question the wisdom of approaching someone who, despite his obvious wealth, cannot significantly invest in the club without removing himself from his ownership position at Newcastle. 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 £4m, 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 indicated 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."
The Union have also expressed their worries that Ibrox could be renamed if Ashley invests further in the club, as he was previously criticised for changing the name of Newcastle's St James' Park to the Sports Direct Arena.
"Finally, 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 knock down 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?"
Ashley took over from Freddy Shepherd as the chairman of Newcastle in 2007.