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The former Chelsea boss has been touted to return to management with either Man United or Paris St-Germain.

But Everton, who now have ambitious billionaire investor Farhad Moshiri on the board, are eyeing Mourinho in case they decide to ditch the Goodison chief.

David Moyes would also be a candidate to return to Goodison – where he was in charge for 11 years – if under-pressure Martinez, 42, loses his job in the summer.

The Daily Star Sunday has been told there is also interest in Southampton boss Ronald Koeman and Ajax’s Frank de Boer.

But bookmakers on Merseyside are taking an increasing number of bets on Mourinho, 53, being appointed, with his odds being slashed from 50-1 to 12-1.

The Special One’s financial demands – £12million a year – could be an issue but Everton have increased financial muscle through Moshiri.

The key to Martinez’s future is Saturday’s FA Cup semi-final against Man United at Wembley.

If Everton win and go on to lift the trophy, Martinez is likely to survive – particularly as Goodison chairman Bill Kenwright is very loyal to his manager.

However he will have to end a run of 21 years if he is to keep his job.