United remain in talks to sign Barcelona midfielder Frenkie de Jong, while the club has also been strongly linked with Ajax winger Antony as Ten Hag looks to build a squad capable of challenging for honours.
The Dutch manager appears to have made an immediate impact, with United beating Liverpool 4-0 in their opening pre-season friendly in Bangkok on Tuesday.
But former United captain Roy Keane insists it will take more time for United to catch up to their rivals and doesn't view them as title challengers this season.
"The manager no doubt will be given money to spend, how he recruits, four or five experienced players have left the club, which I think is a good thing," Keane told Sky Bet.
"But I still don't see United competing with Liverpool and Manchester City, not just yet."
Tottenham have made a number of signings this summer, with Ivan Perisic, Yves Bissouma, Richarlison and Clement Lenglet all arriving at the club, while London rivals Chelsea have also brought in Raheem Sterling and are expected to complete the signing of Kalidou Kouliably from Napoli.
Meanwhile, Arsenal have signed several players including Fabio Vieira and Gabriel Jesus.
But Keane can't see the chasing pack closing the gap to last season's top two.
"I think they will be a bit better. They have quality and the recruitment, but you can't look beyond Liverpool and Man City," he added.
City are going for their fifth title in six seasons and Keane believes they have the edge over Liverpool after signing Erling Haaland from Borussia Dortmund.
"Brilliant players, they've obviously improved with an unbelievable striker [Haaland] and they've got one of the greatest managers ever in Pep [Guardiola]," added Keane.
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Featured Image Credit: Alamy & Twitter/Manchester United
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