According to Morgan, the Chelsea boss wants to stay in London past his stint at Stamford Bridge and offered the Arsenal supporter a 'glimmer of hope' at the GQ Men of the year awards.
The 50-year-old, writing in his Mail Online diary of the awards ceremony, asked the Portuguese manager to give him hope that he will one day manage the Gunners.
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According to the Mail Online's US-editor-at-large, Mourinho said: "Let me put it like this: one day I will leave Chelsea and when I do I will continue living in London,
"There are a number of other opportunities for a manager in London - Fulham, QPR, West Ham, Spurs, the England national team... and Arsenal."
After Morgan had narrowed down the clubs that suited Mourinho's stature, mainly teams in the Champions League, he was left with Arsenal or, alternatively, the England national job.
Morgan went on to say the current Chelsea manager responded 'conspiratorially' saying: "So, Piers, we are left with two options, yes? Arsenal and the England national team."
The former Real Madrid boss then advised Morgan he needed 'patience' after giving him what he wanted, a glimmer of hope.
Having been such a massive part of Chelsea's history in the Roman Abramovich era, it seems unlikely he would switch allegiance from west to north London.
Also, with Arsenal fans demanding a particular style of football at the Emirates, it would be a mixed reaction from supporters should Mourinho ever make the jump across the capital city.
It would seem the two-times Champions League winner was playing with Morgan. Having already stated he would consider managing England, that would appear to be his next career move, if he stays in London.
For now, the Portuguese manager remains at Stamford Bridge and is tasked with changing Chelsea's fortunes after their worst start to a league season since 1988.
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