The Red Devils have added two players to their squad in the January transfer window, signing goalkeeper Jack Butland on a free transfer from Crystal Palace and forward Wout Weghorst on loan from Burnley.
There had previously been a suggestion that United were looking to sign a right-back this summer, with Aaron Wan-Bissaka believed to be nearing the exit door.
However, following a number of impressive performances from Wan-Bissaka, in the absence of Diogo Dalot, plans to sign a new right-sided defender appeared to be put on the back burner.
Dalot has struggled with injury since the World Cup break, and as a result, Wan-Bissaka has started the club's last four Premier League matches, including Saturday's derby victory over Manchester City.
Prior to United's 3-0 win over Bournemouth at the beginning of the month, Ten Hag praised Wan Bissaka for his performances.
"He is doing really well, Aaron, in the last few games. Defending really consistently," the United boss told reporters. "He is also reliable in offence. He has a part in it, he contributes well."
Although Ten Hag has been impressed with Wan Bissaka's performances, United are seemingly keen to sign a new-right back.
According to Tutto Mercato Web, United are currently in discussions with Fulham over a potential transfer for Mbabu.
The report goes as far as to say that negotiations are at an advanced stage for the right-back, who only joined the West London club from Wolfsburg last summer.
With Football London claiming that Fulham are interested in signing Arsenal full-back Cedric Soares on loan, they are open to a potential departure for Mbabu.
Serie A side Monza are also considering a move for Mbabu, but a surprise move from United could end their pursuit.
After joining Fulham last summer, Mbabu has struggled to establish himself in Marco Silva's side, starting only two of his seven competitive appearances.
The 27-year-old has not been included in a matchday since the World Cup break, and now appears to be heading towards the exit door.
Mbabu only made three Premier League appearances in a previous spell with Newcastle United, but he fared better in his time with Wolfsburg, chipping in with three goals and six assists during 82 competitive appearances.