Polish President Andrzej Duda said on Wednesday that a preliminary agreement on the European budget had already been drafted.
Pressure has been mounting on Hungary and Poland over their blocking of the EU's €1.8 trillion budget and coronavirus recovery fund.
"A preliminary agreement is already sketched," he said at a joint press conference with his Czech counterpart Milos Zeman on Wednesday.
"The work and discussions are ongoing, this agreement is the result of very fierce efforts by the Polish and Hungarian parties, but also by the German presidency," he added.
Both countries agreed to the financial package after a marathon summit this summer.
But they changed their position after MEPs pushed to insert a mechanism that would allow the EU to cut off funds to countries that don't respect the bloc's standards.
Now, with a crunch EU summit looming on Thursday, pressure is building on both Budapest and Warsaw to back down.
Radoslaw Sikorski, a Polish MEP with the centre-right European People´s Party group and a former foreign minister, told Euronews that he is glad his country is pulling away from the brink.
"It was absurd to veto a multi-annual budget because you [Poland] don't want to be a law-abiding country... I don't see what Poland has got out of it [the veto], because Poland's interest is to be a law-abiding country," he said.
"It wants to receive support from both the EU budget and the recovery fund," he added.
Watch the full interview with Sikorski in the above video player.
Securing financial support is 'critical' says Germany
Germany currently holds the rotating presidency of the EU. Its Europe minister said further delays to signing off on the fund would be irresponsible.
“The social and economic consequences of the crisis become more visible every day," said Michael Roth. “It would be irresponsible to further delay essential support to our citizens. We need to rapidly unlock the financial support which is so critical for many member states."
It comes as a senior European diplomat warned the other 25 EU countries will have no choice but to sideline the two rebel countries.
They can approve the €750 million pandemic recovery fund without Poland and Hungary, which forms part of the €1.8 trillion package. The €1.05 tr difference, which is the EU's budget for the next seven years, needs the pair's green light.
MEPs pushed for a mechanism to link EU cash to respect for the bloc's values amid concerns Hungary and Poland are not in step with the rest of the continent on issues like media freedom and judicial independence.
But Péter Szijjártó, Hungary's foreign minister, rejected this idea on Tuesday. He said: "It's difficult to interpret science fiction and to have a foreign affairs position from this. All I can say is that the Hungarian position is not new. The Hungarian position has not changed over the years. We reject linking the use of EU resources and common money to unknown and undefined political considerations."
But both countries could end up paying a heavy price if they are left out of the pandemic recovery fund.
"It would mean serious isolation for both countries. And I think it's not far-fetched to argue that it would result in significant domestic crises in both governments on the national stage because it would be very hard to argue why the national economy and even societies are deprived from this essential pot of money," Dániel Hegedűs, an analyst at the German Marshall Fund, told Euronews.