According to the Guardian newspaper, UK officials said that while it was "very early days", some form of extended emergency brake on the free movement of people was "certainly one of the ideas now on the table".
The sources confirmed to the newspaper that despite strong resistance from France, the idea of an emergency brake is being looked at.
The United Kingdom would be able to apply the migration emergency brake for an initial seven years, media noted.
According to the newspaper, such a move would limit the economic shock from Brexit by keeping the United Kingdom in the single market. However, the country would have to pay a substantial contribution into the bloc's budget.
On June 23, the United Kingdom held a referendum to determine whether or not the country should leave the European Union. According to the final results, 51.9 percent of voters, or 17.4 million people, decided to support Brexit, while about 16.1 million opposed it.