Mourinho has already made a huge impact at Manchester United since succeeding Louis van Gaal in the summer of 2016.
Despite the club enduring a rough Premier League campaign last term – finishing sixth – they scooped the Community Shield, EFL Cup and Europa League.
And the Telegraph say talks over a fresh contract are expected to commence in two months’ time.
It is said that any agreement will depend on how Manchester United perform this season – though their 100 per cent record so far bodes well.
Mourinho signed a three-year deal since taking the reins just short of 18 months ago.
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And the Telegraph say United chiefs do not want him to enter the final year of his deal without his future being sorted.
Should the 54-year-old pen an extension then it would be a clear sign that stability could finally be coming back to Old Trafford.
The club have gone through three permanent managers since Sir Alex Ferguson stepped down from the role back in 2013.
David Moyes was the first, succeeding Ferguson after being hand-picked by the Scot himself.
But he was axed just 10 months later after overseeing a nightmare campaign – failing to win a trophy and bringing in one fresh face in the form of Marouane Fellaini.
Louis van Gaal was then appointed as Moyes’ successor.
However, though he won the FA Cup in his final game in charge, United chiefs then decided to replace him with Mourinho, who had been sacked five months previously.