
The club's agents, Rothschild Bank, have been made aware that if a deal isn't agreed by then the pair will pull out.
The two Davids have made it clear that for the Hammers to have any chance of Premiers League - and therefore financial survival - they have to get players in next month's transfer window.
A highly-placed Upton Park source said: "David Gold wanted to end things on Christmas Day but given the business hours difficulties at this time of the year he's been persuaded to extend the deadline.
"Both men want to give Gianfranco Zola the chance to bring in the players who can lift the club away from the relegation zone and they know from their days at Birmingham how difficult that can be.
"If they not have taken control by the 7th they know it will be nearly impossible to get anything done and they aren't going to preside over a club that is heading for financial disaster in the Championship!"
Both men are huge admirers of Zola and his future will be entirely secure under the pair who will hand him an £8million transfer market kitty.
However, they are insistent that if the current feet dragging continues they will pull out of talks which have now been going on for between two and three months
Seventy two year old Gold in particular is deeply frustrated at the lack of urgency in negotiations but has been persuaded to "hang in there" until the seventh.
Said the source: "The two are aware that they are now the only show in town and that the other interested groups have pulled out."
Talks between the two sides continued until late on Christmas Eve and will recommence tomorrow morning.
And a source close to negotiations told Sport of the World: "If I was a gambling man I'd bet on Gold and Sullivan getting control. I'd say things are about 60-40 in their favour.
"There are two answers to the West Ham situation now - a Gold/Sullivan takeover or the Icelandics remaining in charge, following the suspension of their debts, until next September.
"The one certain thing is that the pair will NOT up their bid from the £46m they have tabled. That too has been made crystal clear.
"The Icelandics now have a dilemma. They gamble on things improving at a time when all interest is evaporating, apart from Gold or Sullivan, or trouser the £20 million up front payment they have been offered and get out."
And the source added: "The truth of it all is they are lucky to have anyone interested. This club is not des res and were it not for the fact that David Gold in particular is a Hammers fanatic who was boen across Green Street there would be nothing but a total financial disaster facing the current owners.
"However, Gold is becoming increasingly annoyed and if he sees no real progress over the next few days is certain to pull out."
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