The North-West outfits have endured contrasting fortunes during 2024-25, the latter sitting at the top of the Premier League table when their rivals have decided to opt for a change in direction.
Ruben Amorim has left Sporting Lisbon for Old Trafford and is currently preparing for his first game in charge against Ipswich Town on Sunday.
Nevertheless, with just six weeks remaining before the start of the January transfer window, both clubs will already be contemplating ways to strengthen their respective squads.
Naturally, United will likely be looking at more alterations than Liverpool given their respective campaigns, yet it appears that they both have their eyes on the same target.
Pulisic remains on radar
According to Calciomercato, Liverpool, in particular, remain huge admirers of AC Milan winger Christian Pulisic.
When the United States international left Chelsea for San Siro in 2023, he was eager to kick-start his career after losing his way at Stamford Bridge.
However, the 26-year-old, from a personal perspective at least, is enjoyed the strongest stint of his career, contributing 22 goals and 16 assists from 65 appearances in a Milan shirt.
Six strikes and five assists have come in this season's Serie A and Champions League, Pulisic upstaging previous star man Rafael Leao.
With Pulisic holding a contract until 2027, Milan will soon have a decision to make over how to extend his terms, aware that interest will only increase if he continues on his current trajectory.
Who needs Pulisic more?
West Ham United are also credited as admirers of Pulisic and could offer him a return to London. Furthermore, the Hammers need someone of Pulisic's ability far more than United and Liverpool.
However, there is no realistic possibility of Pulisic choosing to leave Milan for West Ham, making it clear that United are top of the queue for clubs who could benefit from having Pulisic in their ranks.
There are question marks, though, as to whether he would be first choice. As well as the likes of Amad Diallo and Alejandro Garnacho potentially getting the nod under Amorim, the Portuguese sometimes uses inverted wingers or more centrally-equipped playmakers to support the main striker.
In Liverpool's case, Pulisic could be viewed as a straight replacement for Mohamed Salah should he opt not to pen fresh terms at Anfield.