Van de Beek didn't enjoy the best of debut seasons at Old Trafford and spent most of it on the bench.
He is eager to fight for his place in Manchester, but Spanish publication SPORT per Daily Express have said a move was mooted at one point.
The Blaugrana 'studied' sending defender Samuel Umtiti in the opposite direction as a way to balance their books, but United weren't interested.
France international Umtiti has been plagued by injury in recent years and played just 13 times in La Liga last season.
He was once regarded as a top prospect but is now 27-years-old with a poor fitness record.
Barcelona are over budget in regard to their wage bill and need to reduce it to register any new players.
Among their summer arrivals so far are Sergio Aguero, Eric Garcia and Memphis Depay.
Lionel Messi has also agreed terms on a new contract but can't sign it due to Barcelona's inflated squad.
Barcelona finished third in La Liga last season and Ronald Koeman is keen to bridge the gap between themselves and Atletico Madrid.
Meanwhile, United have signed Jadon Sancho this summer and look likely to add to their defense.
The Red Devils are close to signing Raphael Varane from Real Madrid and he's regarded as one of the world's top defenders.
The 28-year-old is entering the final year of his deal and is ready for a new challenge after a decade in Spain.
Madrid have already seen Sergio Ramos depart for Paris Saint-Germain this summer and want a fee for Varane.
United regularly paired captain Harry Maguire with Victor Lindelof last season but are aware they need more experience.
Varane has won four Champions League titles with Madrid as well as the World Cup with France in 2018.
Manager Ole Gunnar Solskjaer was asked about transfers following Sunday's 2-1 win over Derby County.
:speaking_head: "We hope we can announce one player that's been very much written about."- Football Daily (@footballdaily) July 19, 2021
Ole Gunnar Solskjaer says Jadon Sancho's transfer hasn't been a secret but refuses to answer questions about Varane pic.twitter.com/JW83RG0cLH
Sancho is set to be confirmed as United's second signing of the summer after Tom Heaton, but Solskjaer kept his cards close to his chest.
The Norwegian coach told Sky Sports: "There are a couple of things to do with paperwork but we hope we can announce one player who has had a lot written about him. We are working, we want to have a strong squad.
"I don't think it's a secret we have a deal with Dortmund, but until the paperwork is done he is still a Dortmund player."
When asked about Varane, he replied: "Same again."
Featured Image Credit: PA Images
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