Investors and EU officials want European leaders to agree at a March 1-2 summit in Brussels to combine the temporary EFSF with the permanent ESM to create a rescue fund of 750 billion euros ($998 billion).
France backs the idea but Germany has said it is not necessary to increase the rescue fund's size beyond the current 500 billion euros at its disposal.
The permanent European Stability Mechanism (ESM), which is set to replace the European Financial Stability Facility (EFSF), will enter into force in July.
Speaking after French President Nicolas Sarkozy and Belgian Prime Minister Elio Di Rupo met for talks in Paris, the source close to the French presidency said the two governments saw eye to eye on the issue.
"There are identical views on the need to put the ESM into place as quickly as possible and to strengthen it by combining the ESM and EFSF," the source said. "We've already stated that we would return to the question in March and then our German friends will need to be convinced."
"(It is) very necessary that there be strong and high firewalls developed in Europe to deal with fears of contagion," he said.
Increasing the ESM funds is closely tied to boosting the resources of the International Monetary Fund, which Europe says that it wants.
Most G20 countries, which are also the IMF's paymasters, say they first want to see more of an effort by the euro zone to raise funds for its own institutions before the IMF's resources are increased.
Officials, including finance ministers, from the world's 20 largest economies will meet in Mexico City this weekend where they will discuss the IMF's role in trying to resolve the debt crisis. ($1 = 0.7511 euros)