The 18-year-old netted the winning goal when his team secured a 4-3 victory over The Red Devils in the Champions League group stage last November.
This season alone, the teenager has already scored 11 goals in 30 appearances, significantly boosting his market value.
It is understood that Copenhagen are expected to demand a record fee for the Swedish Under-21 international, with estimates hovering around the £17m mark.
His composure and skill in finding the net have apparently not only impressed fans but also Manchester United's scouting team, who were present during his Atlantic Ocean Cup match in Portugal.
According to The Sun, The Red Devils are in search of a right-winger following their decision to part ways with Jadon Sancho to Borussia Dortmund on loan, and Bardghji's consistent performances have firmly placed him on their radar.
The report adds that United's scouts will continue to monitor Bardghji's progress in his club's next fixture against Molde and during both legs of the Copenhagen-Manchester City clash.
Bardghji made a significant impact with Copenhagen in 2021, as he debuted for the senior team just six days after celebrating his 16th birthday. Impressively, he scored his first goal for the club only a week later.
However, when questioned, the winger played down speculation in a recent interview with Sportbladet: «My main focus is here [at Copenhagen],» Bardghji said. «There is not much more to say. All talk is gone. I try to do as well as possible for FCK. I am happy that I am here.
»I also chose to stay here. It feels good.
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