Van de Beek, who joined Ole Gunnar Solskjaer's men earlier this month from Ajax, played his first match for Man United in their 1-0 pre-season friendly defeat against Aston Villa on Saturday.
Goals from Declan Rice and Gabriel Jesus in injury time then sealed a 3-1 comeback win for Arsenal, with Ten Hag's men dropping points again away from home.
However, the Spanish La Liga giants did qualify for the final of this year's Club World Cup after defeating Japanese club Kashima 3-1 that same Wednesday evening, December 19.
The Catalan club also lost 2-1 to Valencia in the Copa Del Rey final last month. Ernesto Valverde's men, however, won the La Liga title ahead of Atletico Madrid and Real Madrid.
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Mourinho said this following Tottenham's Premier League 2-1 victory against Arsenal on Sunday. Mourinho's men defeated the Gunners at home, thanks to two goals from Son Heung-min and Toby Alderweireld.
However, Spurs hit back at Ole Gunnar Solskjaer's men, scoring six times. United are yet to win at Old Trafford this season and are 16th on the table heading into the international break.
City's nearest rivals Manchester United lost 2-1 against Leicester City at Old Trafford, meaning that no club can now catch Pep Guardiola's men, who clinched the title for the third time in five years at the Etihad Stadium.
He also criticized Chelsea's Kai Havertz for missing a vital opportunity to score a goal against Arsenal on Wednesday night at Stamford Bridge as Mikel Arteta's men won 1-0 against the host.
UEFA state that: "A player may be registered on List B if he is born on, or after, 1 January 1999 and has been eligible to play for the club concerned for any uninterrupted period of two years since his 15th birthday (players aged 16 may be