The Red Devils were widely expected to be in the market for a new right-back amid concerns over the futures of Diogo Dalot and Aaron Wan-Bissaka.
Wan-Bissaka had lost his place in the side to Dalot towards the end of the 2021-22 season, and the Portugal international's next career move was also being called into question.
However, Dalot has since cemented himself as Erik ten Hag's first-choice right-back, while Wan-Bissaka remains on the books despite late links with West Ham United.
With Ten Hag having worked with Dest during their time together at Ajax, a reunion was strongly mooted for the 2022-23 campaign, especially with Barcelona seeking to offload the 21-year-old.
Instead of adding a new defender to their ranks, The Athletic claims that Murtough vetoed a move for Dest due to his faith in Wan-Bissaka to win over Ten Hag.
The report adds that Ten Hag would not have stood in Wan-Bissaka's way if he wanted to leave Man United, and there was hope at Camp Nou that Dest moving to Man United could have ushered Frenkie de Jong in that direction as well.
However, the USA international eventually joined Serie A champions AC Milan on loan with an option to buy, but his representatives were supposedly taken aback by Barca's €20m (£17.5m) asking price.
Dest made his debut for AC Milan as a second-half substitute in last week's Champions League draw with Red Bull Salzburg, and the defender remains under contract at Barcelona until 2025.
The American previously came through the youth ranks at Ajax and spent eight years in Amsterdam before heading to Barcelona in 2020, and he has three goals and four assists to show from 72 games for La Blaugrana.
Xavi bolstered his right-back ranks with the signing of Hector Bellerin on a free transfer from Arsenal, while Sergi Roberto, Jules Kounde and Ronald Araujo can also deputise in that area.
Coincidentally, Milan were also tipped to sign Dalot on a permanent deal in the summer after the 23-year-old became a regular for Stefano Pioli during a 2020-21 loan spell.
Dalot has now confirmed that he rejected the chance to move to San Siro in favour of staying at Old Trafford, telling the press: "Milan are a great club and I loved the season with the Rossoneri. But it (transfer) wasn't just up to me. In the end I decided to stay at United and it was the right decision.
"If I'm a better defender I owe it to Milan. Italian football is different from the Premier League and I had to adapt in just one year and playing in Serie A has helped me a lot. Over the past two years here in Manchester, the minutes have increased and, consequently, so has self-esteem."
Dalot has less than 12 months left to run on his current Old Trafford deal, and there have been suggestions that the Red Devils could look to sign ex-Atletico Madrid defender Santiago Arias on a free transfer.