The 54-year-old initially signed a three-year deal with the option of an additional 12 months when he replaced Louis van Gaal in 2016.
United's up-and-down nature on the pitch, coupled with rumours surrounding Jose Mourinho's disappointment at the club's transfer dealings of late, led to mounting reports late a year ago that the Portuguese manager could be eyeing a move to French powerhouse Paris Saint-Germain.
Mourinho has already enjoyed success at United.
The Portuguese tactician is now in his second season with the club, and he has already lifted three trophies - the UEFA Europa League, the League Cup and the Community Shield.
With his career at Old Trafford seemingly all but over at the start of the campaign, Shaw stormed back into Jose Mourinho's plans with a man of the match display against CSKA Moscow in early December.
Fellaini is happy at the club but big money offers from Turkey and China have turned his head and he wants United to raise their opening offer, which he rejected. Manchester United are now hoping for all the formalities to be completed quickly before they announce the agreement, possibly in the next ten days.
He added that his intention was to "bring the club to where the club belongs" and described reports he could leave this summer as "garbage".
The progress being visible on the pitch and off it, Manchester United have been taking steps to tie Mourinho down to a new long-term deal, with his original contract ending in 18 months.