The Red Devils boss had been desperate to reinforce his backline in the transfer window, with the 30-year-old among the players targeted.
It is understood United had been keen to bring Boateng on loan rather than the permanent deal Bayern Munich had been looking for.
The Old Trafford giants had misgivings over his fitness, but the Germany international nipped any interest in the bud during a conversation with Mourinho.
“I had enquiries from Paris Saint-Germain and Manchester United, and I considered them,” he told Bild.
“Not because I wanted to leave Bayern Munich by all means. It was no escape, but rather the thrill of a new challenge.
“I feel completely content at Bayern, one of the biggest clubs in the world.”
He added: “I phoned Jose Mourinho and told him that his interest honoured me and thanked him that he put his back into United for me.
“I explained to him my reasons for not joining.
“It’s difficult to leave Bayern. Everything has to fall in place to top this club, if I do it.”
In an interview to be broadcast with French football show Telefoot due to be aired on Sunday, Pogba seemed to indicate he would be open to joining Barcelona in the future should United decide to sell him.
Since joining up with France’s squad for the international break, Pogba has sparked speculation over his future by suggesting that he could leave Old Trafford as early as the January transfer window.
“I’m playing there at the moment, but who knows what will happen in the next few months,” he said earlier this week before Les Bleus drew 0-0 in their UEFA Nations League opener with Germany.
Pogba has once again rejected the chance to confirm he will see out his contract at United and dropped another hint about his turbulent relationship with Jose Mourinho.
“I’m under contract,” Pogba tells Telefoot in the interview.
“There were little things with the coach [Mourinho], the relationship is always the same.
“We have goals in common, we want to win, that’s all that matters. As long as you do not see me with the Barcelona jersey, it’s because I’m in Manchester. It will always be rumours.”
Barca were keen on signing Pogba in the summer but United rejected an offer of £45 million plus Yerry Mina and Andre Gomes for the midfielder.
Pogba still has three years remaining on his current contract and United also have the option to extend it for a further season until the summer of 2022.
Manchester United left-back Luke Shaw is set to make his first appearance in more than a year for England after he was selected to start Saturday night’s Nations League-clash against Spain (22:45 UAE).
Shaw, 23, had seen his promising career derailed by September 2015’s horrific leg fracture and subsequent mixed relationship with club boss Jose Mourinho.
But the World Cup 2014 call-up has played every minute for the Red Devils this term and impressed throughout.
These star turns were rewarded by manager Gareth Southgate when he chose his first XI since the Three Lions’ surprise run to fourth place in the 2018 edition.
Shaw – who last played for England in March 2017 – missed out on selection for that tournament.
Another player to start the game at Wembley was Liverpool centre-back Joe Gomez. Injury ruled him out of the summer’s event in Russia.
Jordan Pickford; Kieran Trippier, Harry Maguire, John Stones, Joe Gomez, Luke Shaw; Jordan Henderson, Dele Alli, Jesse Lingard; Marcus Rashford, Harry Kane