The consortium has contacted the club's administrators, although no offer has as yet been submitted. The group, which is thought to have wealthy backers and diverse business interests, has been given full access to the club's finances and indicated an intention to lodge a formal bid.
Among the confirmed interested parties so far are Paul Murray, the former Rangers director who fronts the Blue Knights consortium, Brian Kennedy, the Sale Sharks owner, and Club 9 Sports, a Chicago investment firm which failed in bids for Tranmere Rovers and Sheffield Wednesday.
Paul Clark, the joint administrator, described the expression of interest from the Middle East as "credible".
He said. "They are speeding themselves along and expect to make a bid early next week - They're not people I have dealt with before."
Murray remains the favoured option among many fans, since his consortium includes the three main supporters' groups and intends to launch a share issue to allow them some influence. Kennedy, despite describing himself as a "reluctant" bidder, is thought to have made a serious offer.
Some Celtic fans continue to exploit their old rivals' troubles, with the administrators also receiving a bid from a man offering four empty bottles of Irn-Bru, with the accompanying message that they should be redeemed in order to raise the money to buy the club.
The humour was pointed, but following Rangers' 2-1 defeat to Dundee United yesterday, Celtic may clinch the Scottish Premier League title if they win Sunday's Old Firm game at Ibrox.
Murray wants the club's future to be resolved by then, but the administrators believe that is unlikely.
"It's a time for cool heads," said Clark. "We've had bids and we're pleased with them, but there are still several big issues we need to deal with.
"There was comment about whether we could get it resolved before the Old Firm game. That would be very optimistic.
"It will be clearer by that stage, but I don't think the position will be completely resolved.
"We have to work out what each bid means then sit down face to face with the parties, go through it and make sure we know what the deal will look like."
Clark also met Craig Whyte, the Rangers owner, last week, and remains confident that the businessman is not the secured creditor and also that the administrators can take control of his majority shareholding. No sale can proceed unless Whyte agrees to it, or is no longer in charge of the shares.
"We've had ongoing discussions with Craig and I met him just to try and finalise some of these issues," Clark said. "I remain confident that Craig Whyte's position will not be an impediment to a sale - we've had discussions and we think it can be resolved."
Whyte had been linked with a bid for the club from another American investment firm, Fortress, but it is understood he is not formally involved with them. Discussions were held between Whyte and the New York-based company, who are considered serious contenders for Rangers, but they are thought to have been about gaining information on the Ibrox side's circumstances rather than including Whyte in their bid.
Clark said: "Everybody has been sensible and any of the bidders could turn out to be the successful one."