But Pierfilippo Capello insisted his dad would remain loyal to the FA until his deal ends next year.
Pierfilippo, who acts as his father's lawyer and agent, left the door open for a return to Italy after Euro 2012.
Asked if it was true there had been talks with Inter, Capello Jnr said: "Yes. But Fabio will remain with the FA."
Former AC Milan chief Capello, 65, is said to have been offered £20million tax free over three years.
That tops his £6m annual salary as Three Lions manager.
But he felt the loyalty shown to him by the FA after England's World Cup flop should be repaid.
A source told The Sun: "This was a concrete offer and a very attractive one.
"Capello was tempted. But he decided to be loyal and see out his contract.
"He felt he owed England that. Perhaps Inter will come back in a year."
An FA source said: "We've had no contact from Inter Milan and we're confident Fabio will stay."