The 26-year-old was also reportedly given a contract worth around £400,000-a-week to make the move.
The final details are still to be agreed.
The paper adds that the Red Devils hierarchy have been hugely impressed with the way Mourinho has turned around the club's fortunes in less than a year-and-a-half.
United's hopes for the season after their strong start will feel even more promising with those two back in the squad.
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The improved terms are said to be a reward for United sitting joint-top of the Premier League table with rivals Manchester City, with both teams unbeaten after seven fixtures.
He is also likely reaping the benefits of having claimed two major pieces of silverware last season, the EFL Cup and UEFA Europa League.
United chiefs and fans will have no problem with Mourinho staying on at the Old Trafford helm as long as he continues to secure silverware for the club, particularly if he wins a Premier League title.
Owners the Glazer family have made it clear they are willing to back him to achieve that.
The former Real Madrid boss arrived in Manchester last summer, following the sacking of Louis van Gaal.
Now he is convinced United have the closest thing to Sir Alex Ferguson in the Special One.
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