Britain's Home Secretary Theresa May said plans were being drawn to control immigration in the event that Greece exits the eurozone.
"It is right that we do some contingency planning on this [and] that is work that is ongoing," May said.
The Daily Telegraph reported Saturday that the British government was considering what policies might require temporary changes should Greece abandon the euro and adopt its own currency again.
It is expected that a new Greek drachma, if it comes to that, would go through a quick devaluation that would prompt withdrawals from Greek banks as Greeks, trying to preserve the value of their savings, move their money to other countries in the 17-member eurozone.
Similarly, there could be serious repercussions in the labor market, the newspaper said. One of the first possibilities is that many Greeks could lose their jobs in Greece and begin heading to other countries for work.
European law provides for temporary immigration or travel restrictions.
May said Britain was "looking at the trends." However, while the likelihood of a Greek exit from the eurozone appears to increase, there has been no indication that migration from Greece has escalated recently.
It is "difficult to say how it is going to develop in coming weeks," May said.