Under current European rules, a country can close its borders for a maximum of 30 days if it considers there is a threat to public order or security.
France has accused Italy of abusing the Schengen agreement by issuing temporary residency permits to Tunisians, many of whom are likely to head to France.
The Italian government earlier this month granted 20,000 temporary residence permits to Tunisians who crossed the Mediterranean illegally and arrived on the tiny island of Lampedusa.
France is now considering ways to close its borders to keep them out, as many speak French and have ties to friends and relatives in France.
Parliamentarian Chantal Brunel, who earlier this year said that people coming to Europe from the Mediterranean should be put back on their boats, told RFI that the idea of suspending the Schengen agreement is a good first step.
“We cannot allow the entry into our country of hundreds of thousands of illegal immigrants, for whom we unfortunately cannot house or offer jobs to ,” she said.
“We are already unable to give jobs and housing to all of those who are here legally. We cannot, on top of that, give that to illegal immigrants. I think this is a pragmatic policy.”
Last week French authorities stopped trains carrying migrants from coming over the border from Italy.
French President Nicolas Sarkozy is to talk about the issue with Italian Prime Minister Silvio Berlusconi at a Franco-Italian summit to be held in Rome on Tuesday.