One new signing has arrived this summer, with Mason Mount joining the club from Chelsea, but the Red Devils have thus far been frustrated in their attempts to bring in a new number nine.
It is no secret that Man United need a forward, with Cristiano Ronaldo's departure at the end of 2022 leaving a gaping hole in the squad; Wout Weghorst was signed to fill it, temporarily at least, but it did not happen for the Netherlands international during a loan spell from Burnley.
Tottenham Hotspur's Harry Kane is the dream target, with Napoli's Victor Osimhen not far behind, but it is unlikely that either will be signed this summer.
Indeed, Spurs chairman Daniel Levy is not believed to be willing to sell Kane to a domestic rival, while Napoli are thought to want as much as £170m for Osimhen, with the Italian club's president Aurelio de Laurentiis recently claiming that Paris Saint-Germain are the only team capable of affording him.
Benfica's Goncalo Ramos is also admired, as is Eintracht Frankfurt's Randal Kolo Muani, but Rasmus Hojlund has emerged as the team's leading target in the final third of the field.
The 20-year-old scored 10 goals and registered four assists in 34 appearances for Atalanta BC last season in his first campaign in Italian football, while he has netted six times in six appearances for Denmark.
There is an argument that Man United need another forward this summer alongside Hojlund, with Porto's Mehdi Taremi seen as a possible option, and it is not impossible to imagine him arriving at Old Trafford.
Marcus Rashford was comfortably the team's highest goalscorer last season, finding the back of the net on 30 occasions in all competitions, and the Red Devils will again be looking for big numbers from the 24-year-old during the 2023-24 campaign.
Bruno Fernandes was the next highest goalscorer on 14, and it is believed that the 27-year-old will largely feature alongside Casemiro and Mount in a three-man midfield next term.
Anthony Martial was third with nine goals in 29 appearances, but the Frenchman cannot be relied upon due to his injury problems, and it is not impossible to imagine him leaving this summer if Man United sign two attackers.
Alongside Rashford, Antony and Alejandro Garnacho are certain to remain at Old Trafford, but there is uncertainty when it comes to the future of Jadon Sancho.
The England international has found it difficult to show the type of form that made him one of the most exciting forwards in world football at Borussia Dortmund, and a number of clubs are believed to be keeping a close eye on the 23-year-old's situation in Manchester.
Ten Hag also needs to make a decision on Amad Diallo, who excelled on loan at Sunderland last term, but the 21-year-old should be given the whole of pre-season to make a case for a first-team spot.
Facundo Pellistri is in a similar situation, with the Uruguay international potentially leaving on loan this summer in search of regular football, which is required at this stage of his career.
Anthony Elanga is heading for the exit door, while the two goalscorers from the team's opening pre-season friendly of the summer against Leeds United last week, Noam Emeran and Joe Hugill, are unlikely to be a part of the first team during the upcoming campaign.
A final decision on Mason Greenwood is believed to be close, but it is unlikely that he will be a part of the squad next season, with a loan move to a foreign league thought to be the expected outcome, with the 21-year-old set to rebuild his career away from Old Trafford, at least temporarily.
Rashford, Sancho, Antony, Garnacho and Hojlund would be an impressive group of players for Ten Hag to choose from in the final third of the field, but it is glaringly obvious that an experienced head is needed at centre-forward.
Man United are right to move on from Kane, and Taremi, who has scored 80 goals in his three seasons at Porto, might be the perfect acquisition, with his contract due to expire next summer.
Ten Hag's side are currently preparing for their second friendly of the summer against Lyon on Wednesday, and they will then head to the United States for friendlies with Arsenal, Wrexham, Real Madrid and Borussia Dortmund.