The versatile defender had been interesting Manchester City until their rivals beat them to his signature following a trial at Old Trafford.
Still, United's inability to sign a new centre-back - Leicester City's Harry Maguire and Tottenham's Toby Alderweireld seemingly topping the wishlist after a move for Yerry Mina failed - has left the Portuguese boss anxious about the season ahead.
Manchester United are chasing a center-back this season, and have reportedly been in talks with Barcelona star Yerry Mina, but Boateng could be their next target as Jose Mourinho looks to strengthen his squad ahead of the new Premier League season.
"I found out that Martial was going to Paris when he told me", said Mourinho at the time.
Jose Mourinho fears Manchester United are in for a "difficult season" if he is unable to add to his squad before Thursday's deadline.
"I know that he tries his best for me".
The France international's future has been a source of relentless speculation over the past few months following a hard second season under Jose Mourinho.
Martial has just one-year remaining on his current deal with United, who have the option to trigger a year extension, and having forked out £44m to date for the forward, United value him at £80m - a figure which has put off potential suitors from elsewhere across Europe.
Mourinho wants two signings to turn United into Premier League champions.
"In every pre-season it happens the same, with every club, which is that the manager wants more".