The Red Devils are currently enjoying one of their strongest campaigns for some time, already lifting the EFL Cup and reaching the latter stages of the FA Cup and Europa League.
Furthermore, Erik ten Hag's side look likely to finish in third position in the Premier League standings, closing the gap on the likes of Arsenal and Manchester City ahead of 2023-24.
Nevertheless, United are expected to be active during the next transfer window with extra competition and depth required in several areas of the pitch.
One position of concern is central midfield, with Casemiro the standout figure but without other players to match his qualities when he is not in the team.
As it stands, that responsibility either falls to Fred or Scott McTominay, with the latter having fallen down the pecking at Old Trafford this season.
With McTominay potentially on his way out of United in the summer and there no guarantee over the future of Bayern Munich loanee Marcel Sabitzer, the English giants may find themselves requiring two fresh faces.
According to Telegraf, United have initiated contact with intermediaries regarding the availability of Grujic.
The Serbia international is no stranger to English football having spent three years contracted to Liverpool, making a total of 16 appearances.
However, the 26-year-old has enhanced his reputation during his time with Porto, making 94 outings for the Portuguese giants since his arrival in 2020.
The report suggests that any potential deal may be hampered by Grujic's loyalty to Liverpool, who he supported during his childhood.
Nevertheless, it appears that United are open to signing Grujic, despite the player still having over three years remaining on his Porto contract.
AC Milan are also said to be monitoring the situation, although it is not suggested what fee Porto may demand if they are to consider a sale later this year.