Another goalkeeper is still expected to arrive due to Dean Henderson's loan switch to Nottingham Forest, while the club remain in talks with Barcelona over Frenkie de Jong.
Ajax attacker Antony is also still allegedly a target, although it remains to be seen whether the 20-time English champions can come to an agreement with the Dutch giants over a transfer fee for the Brazil international.
Man United have already taken advantage of the free agent market to sign Eriksen this summer, and there are still a number of high-profile players available for nothing in the current market.
With that in mind, Sports Mole picks out three players that the Red Devils could sign following the expiration of their contracts at their respective clubs.
Andrea Belotti
Andrea Belotti's contract at Torino expired at the end of June, and the 28-year-old remains a free agent despite the ongoing speculation surrounding his future.
The Italy international enjoyed a strong 2021-22 campaign for his Serie A club, scoring eight times and registering one assist in 23 appearances in all competitions.
Meanwhile, in total, he netted 113 goals and registered 28 assists in 251 appearances for Torino, with his scoring record making him an attractive proposition for a number of leading European clubs.
Man United are still battling to keep of Cristiano Ronaldo, but they remain short at centre-forward following Edinson Cavani's departure.
Anthony Martial has been in impressive form during pre-season, scoring three times in three matches, but if Ronaldo departs, the Red Devils will have to enter the market for a new striker, and Belotti, who is currently being linked with Juventus and Roma, could be considered by Ten Hag's side.
Dan-Axel Zagadou
Man United are currently well-stocked in the middle of their defence, with Martinez joining to provide competition for Victor Lindelof, Raphael Varane and Harry Maguire.
Eric Bailly, Axel Tuanzebe and Phil Jones could all move on, though, so it would not be a shock to see another central defender arrive at the club in the current market.
Man United were linked with Dan-Axel Zagadou earlier this summer, and a recent report claimed that the Red Devils still have a genuine interest in the Frenchman.
The 23-year-old is available on a free transfer following the expiration of his contract at Borussia Dortmund, who he represented on 91 occasions in all competitions.
Zagadou played 67 times in the Bundesliga and 14 times in the Champions League during his time at BVB, and the former Paris Saint-Germain youngster will certainly not be short of offers.
Florian Grillitsch
Man United are still attempting to bring in Frenkie de Jong, but a recent report claimed that Leicester City's Youri Tielemans is also a target for the Red Devils, who are expected to sign at least one midfielder before the end of the transfer window.
Eriksen has arrived on a free transfer, but the Denmark international is likely to operate slightly further forward, while Ten Hag has said that he views Donny van de Beek as a number 10, so the team's options in the two central midfield positions are limited following the departures of Nemanja Matic and Paul Pogba.
Florian Grillitsch was linked with the Red Devils earlier this summer, and the 26-year-old is now a free agent due to the expiration of his contract at Hoffenheim.
The 33-time Austria international, who largely plays as a defensive midfielder, only made 18 Bundesliga appearances last season, missing the end of the campaign with a muscular problem.
Grillitsch made 150 appearances for Hoffenheim before departing, while he also represented Werder Bremen on 54 occasions between 2015 and 2017, and at 6ft 2in, he would be a towering presence for the Red Devils, who would surely have to move quickly in order to secure his signature amid the growing competition.