The withdrawal of financial support is a further blow to Green, since supporters are refusing to buy season tickets for the forthcoming campaign until he sells the assets to Smith's consortium. Fans are also planning a rally in support of the former Ibrox manager's bid.
The first major sponsor to withdraw is Central Car Auctions, major financial supporters of Rangers for more than 35 years. The Glasgow-based company has a corporate box at the stadium as well as prominent signage, and is thought to invest a six-figure sum.
That will not continue while Green's consortium remains in charge, increasing the financial pressures on a group that has struggled to pull funds together. Green's investors will not put more of their own money in, since their intention is to quickly sell up, yet running costs still need to be met.
Jonathan Miller, owner of Central Car Auctions, said: "I'm not going to do sponsorship just now, because I have a fear factor about Mr Green. He's there for the sole reason of making some money, then walking away. After what's happened with Mr Whyte, it's a total embarrassment.
"I feel strongly about it. We've been sponsoring things at Ibrox for more than 35 years, boxes and we now have our signs there. We still have a contract for another year, but because of what's happened, that contract won't stand now.
"I just feel that somebody's got to do something. He's got a similar look to him as Whyte, he's just there for the money. The biggest thing in this is Walter [Smith]. If he says 'don't renew your season tickets', nobody will. [Green] is [looking to be] in and out for a quick kill. Fingers crossed, it will all get sorted."
Herald Sport understands that a taxi firm will also withdrawing sponsorship of around £70,000. While Malcolm Murray, the new chairman, claims Green's consortium have a long-term plan, the real intention is to sell the business on quickly.
Smith's consortium, backed by Douglas Park, the transport tycoon who was a major sponsor of the Ibrox side, and Jim McColl, one of Scotland's richest men and head of the Clyde Blowers engineering firm, made a £6m bid on Thursday, just before Green's consortium bought the business and assets from the administrators, Duff & Phelps, for £5.5m.
As well as refusing to renew season tickets, Rangers fans are planning a march and rally on Saturday, June 23, in support of the consortium fronted by Smith, the two-time manager of Rangers who would become chairman if they successfully complete their proposed takeover.