The 20-time English champions were strongly linked with the Villarreal defender earlier this year, and they had been expected to bring him to Old Trafford for the 2022-23 campaign.
However, Man United have instead boosted their defence with the arrival of Lisandro Martinez, who starred under Ten Hag at Ajax.
According to The Mirror, the Red Devils had been set to sign Torres when the summer transfer window opened for business, only for Ten Hag to overrule the club's recruitment department.
The report claims that Ten Hag's strong relationship with Martinez played a key role in the club signing him ahead of Arsenal, who were also keen to bring him to the Premier League.
Torres, who is currently being strongly linked with Juventus, allegedly came close to joining Tottenham Hotspur last summer but decided to remain at Villarreal in order to represent the club in the Champions League.
"Right now there is nothing at all, there is talk of many things like every year, I have peace of mind of being where they want me, at the club of my life and I have this offer right now that I value as very positive", AS quoted Torres as saying when addressing his future earlier this summer.
"There is nothing right now, the only thing I have is the offer from Villarreal, so I am very calm."
The Spaniard made 47 appearances for Villarreal last term, contributing six goals and one assist in the process, playing a key role in the club reaching the semi-finals of the Champions League.
"The pull of playing the Champions League with the team from my town was bigger," Torres told The Guardian last year when asked why he decided to reject an exit in the summer of 2021.
"I was clear from the start. This is only the fourth time Villarreal reached the Champions League, which shows how hard it is, and it was a dream to play in the competition with my lifelong club."
Victor Lindelof, Harry Maguire, Raphael Varane and Martinez are expected to be Man United's four central defenders next term, with Phil Jones, Eric Bailly and Axel Tuanzebe potentially moving on.
The Red Devils have also boosted their defence with the arrival of Tyrell Malacia from Feyenoord, while it is being reported that the club are closing in on a deal for Lens defender Jonathan Clauss.
Man United will play their final two pre-season fixtures of their Australia tour against Crystal Palace and Aston Villa before heading back to Europe for friendlies against Atletico Madrid and Rayo Vallecano.
Ten Hag's side, who have also brought in Christian Eriksen this summer on a free transfer, will open their 2022-23 Premier League campaign at home to Brighton & Hove Albion on August 7.