Trade and Industry Secretary Stephen Byers is expected to ask the German car giant to extend this Friday's deadline for bids for Rover.
His appeal will be echoed tomorrow by Rover union leaders who will take their plea for an extension of the deadline to BMW's head office in Munich.
BMW has indicated it is on course to sell Rover Cars to venture capitalists Alchemy.
But it is being asked to allow more time for a bid from rival consortium Phoenix, headed by former Rover chief executive John Towers, to be finalised.
Bill Morris, general secretary of the TGWU said: "Alchemy have had six weeks to work up their financial package.
"The Towers team should be given the same opportunity. If successful the Towers team will secure the jobs of thousands in the Midlands but they must be given an opportunity.
"BMW has a moral and social obligation to the UK workforce and their families and they must listen to the Towers team."
Tony Woodley, chief Rover negotiator for the TGWU, added: "BMW is making it impossible for Mr Towers because they want to see cash up front, but you cannot get money until you have carried out due diligence."
The Towers' proposals are said to include production of up to 250,000 cars each year, with 1,000 to 2,000 redundancies from the 9,000 strong workforce - less than half those thought likely under the Alchemy plans.
The scale of job losses in the West Midlands from the sale of Rover's Longbridge factory is to be disclosed later this week.
The taskforce set up by Mr Byers to look at ways of regenerating the region will present its interim report which is expected to warn of thousands of job losses among suppliers and firms which service Rover.