The German defender was the topic of transfer rumours throughout the summer window, but opted to remain with Bayern for his eighth season with the club.
Manchester United might prefer to sell Martial to a club that isn't in the Premier League and newspaper reports actually suggested that Paris Saint-Germain turned down the chance to sign Martial for £70m in the summer because of his high wage demands.
Mourinho was adamant on bringing another centre-back to Old Trafford, with Harry Maguire also viewed as a target.
Boateng, 30, looked set for an exit from the Bundesliga champions in the previous transfer window with Paris Saint-Germain and Manchester United both lodging bids for the 2014 World Cup victor.
And Boateng confirmed that the former Frankfurt coach was one of the factors keeping him.
Bayern Munich's Boateng had already made his stance clear on the transfer as he personally called Mourinho to rule himself out of any potential deal.
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"I had enquiries from PSG and Manchester United", he told Bild.
The 30-year-old has been at Bayern since 2011, and has represented the club on 261 occasions so far. It was no escape, but rather the thrill of a new challenge.
"As a fan, honestly, part of me is that no one is bigger than the club and I am not interested in people who are looking left and right".
"I explained to Jose that it's hard to leave Bayern, and if I do, everything has to be in place to top this club".
The experienced defender has won 6 Bundesliga titles, 4 domestic cups and the Champions League during his time at the Allianz Arena while he also helped lead Germany to the 2014 World Cup.
Manchester United lost back-to-back matches earlier in the season but bounced back with a 2-0 victory over Burnley before the global break.