Employers are to propose a joint approach to ministers to secure extra Whitehall cash to fund the fresh award during knife-edge negotiations with the Fire Brigades Union.
But Andy Gilchrist, general secretary of the FBU, said he was not prepared to receive a conditional offer and suggested that any deal had to be above the 16% over two years floated last summer.
"They understand how they can avoid this strike and they know how they can do it," he said. "November is not July. Our pay claim remains in place, as does the strike."
John Ransford, a director of the Local Government Association, said that a "substantial offer" was on the table and he wanted to negotiate although he refused to be drawn on the figures.
"The employers are taking every opportunity and leaving no stone unturned to try to put an offer to the FBU which is fair to everyone concerned," said Mr Ransford.
Today's talks follow the failure of the council team to table a new offer yesterday. Senior figures on the council team instead agreed to propose an unlikely alliance with the union to persuade Downing Street to reverse its insistence that no more money would be made available to end the dispute.
No 10 said the "public spending envelope is sealed" to limit the room for manoeuvre by the employers, insisting any improvement in a rejected 11% over two years had to be financed from modernisation or efficiency savings.
"In terms of giving money from one department to another, are people suggesting that to fund a hyper-inflationary pay award, not linked to modernisation, we should take that money away from schools, hospitals, the transport system? There is no free money."
The deputy prime minister, John Prescott, has indicated there is scope for a higher offer, including a jump in the 4% proposed this year, and a three-year option has been indicated.
But time is running out to halt the strike after the FBU, which has ditched its original 40% demand, said an offer of 16% over three years, which was floated during discussions, was insufficient.
FBU negotiators spent four hours yesterday waiting in a central London hotel for a telephone call to invite them to resume formal negotiations half a mile away in a suite of rooms used by the employers.
When Mr Gilchrist's mobile phone finally rang shortly after lunch, it was to arrange a meeting today - less than 24 hours before the strike is due to commence. The unexpected delay effectively lost a day of talks. "We have always been prepared to look at a serious offer on pay. We have not had one," Mr Gilchrist said last night. "The ball is now firmly in the employers' court."
The two sides have each published their own proposals to reform the fire service as Sir George Bain's government appointed review is sidelined in the search for a solution.
Three of the employers' four key elements - leaving fewer firefighters on duty at night, ending an overtime ban and merging control centres - are opposed by the union which has reservations about the fourth, the extended use of defibrillators.
Counter proposals from the FBU would cost more money in the short term before delivering savings, including a new community safety initiative, while others, such as station creches and career breaks, have not been received enthusiastically by employers.
Meanwhile, West Yorkshire fire authority faced calls from the FBU last night to disclose the salaries of its four most senior officers after it emerged that they shared a £77,000 increase last year.
And a leader of the fire service in Northern Ireland, significantly more sympathetic to the FBU campaign, complained that she had been frozen out of the negotiations. Rosemary Craig said yesterday: "When they come in to begin negotiating I'm put out of the room."
