
Former Chelsea boss Mourinho, 44, has been gainfully unemployed since departing from Stamford Bridge in September.
The formidable Portuguese manager was the bookies early favourite for the role, but it is understood that the ‘Special One’ would rather wait for a vacancy at a major European club to become available.
Radio 5 Live's football correspondent Jonathan Legard said: "Mourinho is apparently champing at the bit to return to football management.
"But not for a job, however lucrative and high profile, that only allows him to do what he does so well - working with players - a couple of times every few months.
"He's like a lion in a cage, I was told, but a national job, even such a special post like England, would only appeal at a later stage in his career and the chances are even then that would only be the Portugal job.
"Far more attractive for the former Chelsea title winner at the moment is a top European club vacancy and as he waits for that, so the FA must come to terms with the size of their task."
The Football Association's chief executive Brian Barwick has begun his search for a replacement for McClaren, who was sacked on Thursday after England failed to reach Euro 2008.
Many names have been thrown into the debating ring, including Fabio Capello, Harry Redknapp, Sam Allardyce and Martin O’Neill.
But ex-Manchester United and England player Paul Ince believes the FA should re-appoint Glenn Hoddle.
The 50-year-old was England boss for three years before being sacked in February 1999 after suggesting that disabled people were being punished for sins in a previous life.
Ince told BBC Radio 5 Live: "I wouldn't look any further than Hoddle. He did a very good job and he wasn't sacked for footballing reasons.
"The FA has got to forget about what happened years ago, they've got to be bold and brave.
"Hoddle is sharp, bright, meticulous and he's English, but whether the FA is prepared to go back is not my decision."
Sportpen.net