France was the first country to join the US-led coalition in air strikes on ISIL insurgents in Iraq, who have also taken control of large parts of neighboring Syria during the course of the three-year-old civil war there.
"We are thinking about a deployment in Jordan," Army spokesman Gilles Jaron told reporters, adding that it was being discussed with authorities in Amman.
"It would reduce time in the air between take-off and missions above Iraq," he said.
It currently has nine fighter jets, maritime patrol aircraft, a refueling plane at its base in the United Arab Emirates as part of its "Chammal" Iraq mission, as well as a war ship in the Persian Gulf.
Two French diplomats said putting jets in Jordan would also help reduce costs at a time when the government is under pressure to cut spending and this week was forced to find ways to fill a 600 million euro budget gap in additional costs for overseas military operations.
"It would be quicker and save money," said one French diplomat. "It's in our interest to be as close to Iraq as possible." A second source said a decision would be made this month.
France has given Iraqi Peshmerga fighters weapons and training, but has ruled out carrying out air strikes in Syria.