Mr Fischer announced over the weekend that he was throwing his hat into the ring, challenging frontrunner Christine Lagarde, France's finance minister, and Mexico's central bank governor Agustin Carstens. Mr Fischer is a well-liked former deputy head of the IMF.
"One problem is his age. Fischer is 67, which is two years older than the demands for the position," Yuval Steinitz, Israel's finance minister said.
Current rules restrict the appointment of anyone over the age of 65 and dictate that no-one can hold the five-year job beyond the age of 70.
"I hope they find a way around it, it's not a suitable criteria in this day and age," said Mr Steinitz but added that Mr Fischer's chances were "not great".
The IMF's executive board meets today to discuss who will succeed Dominique Strauss-Kahn, who resigned following his arrest last month on charges of attempted rape. He denies the allegations.
As a dual Israeli-American citizen, there is also the question of whether Mr Fischer's nationality could hamper his chances, as the top IMF job usually goes to a European.
Economist Nouriel Roubini said Mr Fischer was a perfect candidate but would find it difficult to derail Ms Lagarde's campaign. "At this late stage, he does not have enough support to succeed," he said.
Mohamed El-Erian, co-chief investment officer at Pimco, the world's largest bond fund, also praised Mr Fisher's credentials. "He is extremely well liked by the staff of the IMF, well known and genuinely respected by the member countries of the institution."
On Sunday, G20 member Indonesia backed Ms Lagarde for the role, the first public endorsement from a major emerging market. This was closely followed by that of Egypt.
Europe has come out in force for Ms Lagarde, as it struggles to keep the IMF-led bailouts of Greece, Ireland and Portgual on the rails.
The United States and Japan, the IMF's other power brokers, remain publicly uncommitted.
The pullout of two other potential candidates - Grigory Marchenko of Kazakhstan and Trevor Manuel of South Africa - underscores the widespread belief that Europe already has a done deal.
Article from Telegraph