The 33-year-old, who won eight caps for England, was forced to retire last week because of a shoulder injury and consequently had his contract cancelled by his club Sale.
Fourie, whose 18-month-old son Hendro was born in England, has been in the country for eight years, and also played for Rotherham and Leeds. "We have not curtailed Mr Fourie's visa at this time and he is not required to leave the UK," a UK Border Agency spokesman said.
"His employment contract with Sale Rugby Club has been terminated and his employer has rightly informed UKBA of this decision. We are considering what action to take next.
"If an individual's circumstances change and they no longer meet the terms of their specific visa they can apply for a visa of a different type.
"Mr Fourie has been informed of the process and the various options available to him. It is entirely up to him if he chooses to explore any of them further."
England head coach Stuart Lancaster has expressed his relief that Fourie can stay in the UK.
He said: "I'm pleased that I hear over the last 24 hours that some flexibility is going to be shown. I spoke to him only last week - he was a player I signed for Leeds from Rotherham and he was outstanding, he was the best signing I made. He was unbelievable."
He added: "It's massively disappointing he has lost his chance to further his international career and his club career as I thought Sale had made a brilliant signing."
Lancaster said from his talk with Fourie the prospect of returning to South Africa was also "quite attractive" to him".