There have been no new confirmed cases for 16 days
Tests are being carried out at a farm west of Carlisle in Cumbria.
If confirmed, it will be the first new case of the disease for 16 days.
Earlier, Mrs Beckett said that increased movement of livestock during the autumn could create a real danger of a resurgence of the disease.
"I would almost say it would be a miracle if we got through the period of the autumn movements without seeing a resurgence," she told the Commons' Environment, Food and Rural Affairs Committee.
"There must be a real danger."
Last month Mrs Beckett announced a licensing system allowing pigs, cattle and sheep to be moved under a variety of conditions, depending on the risk levels in a particular area.
Blood tests
The implementation of the system had been delayed due to computer problems but these had now been ironed out, she said.
Government chief vet Jim Scudamore told the committee that a minimum of three months had to pass without further confirmed cases before an application for disease-free status could be considered.
Mr Scudamore added that blood tests might have to be carried out on sheep for a more than year after the final case to make sure the virus was not being carried in flocks which had not developed the disease.
'Bad luck'
Mrs Beckett took the opportunity of her appearance before the committee to again reject calls for a public inquiry into the foot-and-mouth outbreak.
"There is a growing modern culture that if anything goes wrong someone must be to blame, and we have to find that person to blame and pillory," she said.
"It seems to me that a lot of things happen as a result of chance and bad luck and often there isn't anybody to blame, and most of the time most of the people are trying to do their best."