Interior Minister Manuel Valls, who has overseen the dismantling of several camps and the repatriation of hundreds of Roma, said the lifting of labour
market restrictions "could be one of the solutions" to what has been a divisive issue for the Socialist administration.
It will be discussed next week at a ministerial meeting chaired by Prime Minister Jean-Marc Ayrault.
France is one of a number of European Union countries which declined to grant Bulgarian and Romanian workers unrestricted access to their labour markets following the two countries' accession to the EU in 2007.
Critics of that policy argue that it puts Roma migrants in an invidious position since they can be deported because they cannot demonstrate that they
can support themselves but at the same time, cannot seek work legally.
One of the EU's founding principles is that citizens should be able to work in any member state and the transitional arrangements permitted when Bulgaria
and Romania joined must be phased out by the end of 2013.
France's move to possibly bring that forward follows criticism of Valls' policy from sections of his own party, from Green members of the government
and from Roma rights groups.
Socialist MP Pouria Amirshahi said the government's change of tone on the issue was long overdue.
"At last!" he said. "At last this issue is going to be looked at through an optic other than one of police repression."
Valls' critics have accused him of continuing the policies of former President Nicolas Sarkozy, who sparked international outrage in 2010 when he launched a sweep of Roma camps that resulted in hundreds being repatriated.
Sarkozy's actions and rhetoric prompted a threat of legal action from the EU's executive arm, the Commission, and prompted Justice Commissioner Viviane
Reding to warn that France was reviving unhappy memories of World War II deportations.
The Commission said last week that it was monitoring the new government's handling of the Roma but has stopped short of accusing the administration of
breaking any EU rules.
Valls said that a commitment made by President Francois Hollande during his election campaign that camps would not be dismantled without rehousing options having been put in place would be honoured eventually.
"It will take time," Valls said. "The objective will be met progressively but it is difficult and we have to acknowledge that."
Valls last week sanctioned the dismantling of camps on the outskirts of Lyon and around the northern city of Lille which were home to more than 250
On Tuesday, police in Lyon removed 46 Roma, including 25 children, from a squat in the city centre.
The Socialists have also continued their predecessors' practice of offering Roma financial incentives (300 euros per adult, 150 euros per child) to be
flown back to their native countries.
Critics say this is a waste of public money as there is nothing France can do to stop Roma from immediately coming back.
Polls suggest the government's treatment of the Roma enjoys wide support with as many as 80 percent of voters supporting the dismantling of camps, even
almost as many (73 percent) accept that this moves rather than solves the problem.