Sportsmail reported last week that the 29-year-old had been offered to United after his move to Paris Saint-Germain collapsed.
To me, he's one of the best central defenders in the world'.
United's build-up to the new campaign has been dominated by Mourinho's clear frustration over transfers, which has brought his relationship with executive vice-chairman Ed Woodward into the spotlight.
'I hope he'll stay with us because he's an important player.
Rashford donned the famous shirt for the first time on Sunday evening, as United fell to a 1-0 defeat to Bayern Munich in their final match of pre-season.
The other clubs that compete with us are really strong and already have fantastic teams and squads, like Chelsea, Tottenham, Manchester City, or they are investing massively like, for example, Liverpool, that is buying everything and everybody.
It has been suggested that the Portuguese tactician is happy to part ways with Martial following his decision to leave United's pre-season tour of the USA to be with his partner for the birth of his son, Swan.
Mourinho wants two new players before Thursday's transfer deadline - a centre-back and a right winger - but has privately conceded one new arrival is more realistic.