However officials at the governing body have been keen to stress that no one has yet been approached formally to take the job.
"To be manager of England is not the same as being manager of another country," Eladio Parames, Mourinho's adviser, told Sky Sports News. "To be manager of England is a big job, a very interesting job and every coach would be honored to be invited."
"I can't say whether he is interested or not but he loves English football and he loves the crowds, so I am sure he would consider it," Parames said.
Mourinho quit Chelsea in September.
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