Rangers fans' group Sons of Struth will ballot its 1,500 members in the next 24 hours on boycotting home matches in protest at how the club is being run.
The group's co-founder Craig Houston told BBC Scotland fans are concerned about recent developments at Ibrox.
He says they are angry that who is wanted by Interpol for finance crimes.
And the naming rights for Ibrox has caused further dismay.
"We'll be putting it to our members and asking them to decide if they wish us to do something," said Houston.
"We might not do any [boycott], we might do one game or we might go for the whole season, but our club should not be in this position.
"We put out leaflets at a game over a year ago suggesting that Rafat Rizvi was involved in investing in the club back then.
"We've been asking as fans for over a year now to tell us who these faceless investors who are running our club are.
"We don't get any answers and because this man pops up again - miraculously, coincidentally - that has raised a few eyebrows within the Rangers support.
"And we seem to have sold our naming rights to our stadium for £1; the fact that it's been sold is one aspect, but the worst aspect is the £1."
Sons of Struth's move follows Wednesday's opposition by supporters' group Union of Fans to Rizvi's involvement with the Championship club.
Rangers deny that Malaysian Datuk Faizoull Bin Ahmad is considering investing. He visited Ibrox Stadium and the club's Murray Park training ground and had lunch with Easdale and Rizvi.
Houston also indicated that fans could consider a boycott of Sports Direct, the sportswear retailer owned by Rangers shareholder Mike Ashley.
He said the key thing the fans want is transparency, something "we've been asking for the 12 months of our existence".
Asked if he was concerned that a boycott could threaten Rangers' future, Houston said: "This board, who have been placed by the same people that have placed every board member in Ibrox since Charles Green's time, have got the blood on their hands should Rangers go into administration, not the fans.
"The fans have given these people 100,000 season tickets over three years, they gave them £22m in IPO, they've bought shirts and merchandise.
"We were filling stadiums in the bottom tier of Scottish football.
"So for anybody to suggest that Rangers fans, if they take an action of boycotting, are in any way to drive that final nail in the coffin, I would suggest they are looking in the wrong place."
BBC Scotland asked Rangers to comment on the boycott threat, but has yet to receive a reply.