"If the entire movement asks for it, I will run. I would consider it a common effort, where I can be the standard bearer," Joly said.
"It is important for the visibility of the [Green] party, for the Socialists and the political left, and we could surprise. This should not be underestimated."
Joly, 66, was elected as a member of the European Parliament in 2009 with Europe Ecologie, but is best known as the investigator who exposed fraud at the French oil company Elf.
An embattled Sarkozy has been grappling with plummeting approval ratings, with unemployment and economic woes topping the agenda as France goes about implementing reforms to reduce its swollen deficit.
The main opposition Socialist Party will choose its challenger to Sarkozy next northern summer, with a large field of potential candidates including International Monetary Fund head Dominique Strauss-Kahn.