"I want a mention of a sum... let's see what is possible, it's coming close to the decisive moment, we're not ready yet," said Reinfeldt, whose country holds the rotating EU presidency.
He hoped his colleagues would use the summit as an opportunity to reach agreement and overcome resistance on the issue, which remains strong in many eastern European countries.
"I also want a mention of the sum because it's needed for other developed countries," he added, ahead of the two-day summit in Brussels.
While the leaders have already agreed on broad objectives for reducing greenhouse gas emissions, vowing to cut them 20 percent by 2020, they are split on how to share the costs for such efforts, both within and outside Europe.
The European Union is keen to enter international climate talks in Copenhagen in December speaking with a unified voice to encourage the rest of the world, particularly the United States and China, to commit to sweeping emissions cuts themselves.
However the question of how to help developing nations pay for action against climate change remains a major bone of contention, with poorer central and eastern European countries showing little enthusiasm to put their hands in their pockets.
The European Commission estimates that €100 billion ($147 billion) will have to be found annually by 2020, with €22-50 billion of that to be found from public coffers.
The commission hopes that Europe's contribution will reach up to €15 billion per year in the 2013-2020 period, and is also calling for €1.5 billion to be provided annually as fast start up money for 2010-2013.
While environmental groups argue that would be insufficient, some countries argue that their cupboards are already bare due to the economic crisis which plunged Europe into recession and has left many with massive public deficits.
"In the current form, the burden-sharing proposal is not acceptable to us," said Hungary's Prime Minister Gordon Bajnai, adding that this view is shared by Bulgaria, the Czech Republic, Latvia, Lithuania, Poland, Romania, Slovakia and Slovenia -- all newer members who have joined the EU since 2004.
A major problem in deciding who pays what is the balance to be found between charging the richest nations and charging the most polluting nations.
Eastern countries, led by Poland and its coal-fuelled power stations, say they will be overly penalized if too much emphasis is put on emissions, arguing that the more developed western European nations have already benefited from unfettered pollution levels and should fork out for the changes.
Others argue that Europe should wait to see the results of the Copenhagen talks before it decides on its own contributions in too much detail.
Sweden's European Affairs Minister Cecilia Malström sought to minimize the consequences of a failure to reach a unanimous deal in Brussels.
"We still have time," before the Copenhagen talks start on December 7, she said on the margins of a pre-summit meeting of European liberal leaders.
Others in Brussels displayed more urgency on the climate funding issue.
"The time has come when the EU has to put money on the table," said Danish Prime Minister Lars Lokke Rasmussen.
"Some of my colleagues think we should wait for tactical reasons, that we keep our wallet in our pocket," but that would risk undermining Europe's position at the head of the climate talks, he argued.
"We could keep this leadership if we put money on the table," he said.
Finnish PM Matti Vahanen agreed: "I really hope we can do it because the EU will have its summits with US, China and India during the next few weeks and it will be good that we have some concrete figures on the table. We have to say that we are really committed to finance developing countries."