The Red Devils are expected to assess their options during the winter transfer window after a difficult start to the campaign, with several areas of the squad under scrutiny.
According to transfer journalist Matteo Moretto, United have contacted the Spanish clubs to ask about the availability of López and Barrios.
Moretto stressed that there have been no negotiations, with the approaches amounting to initial enquiries rather than formal attempts to complete either transfer.
Both players would be difficult to prise away from their current clubs. López has become an important attacking option for Barcelona, while Barrios is a regular part of Diego Simeone's plans at Atletico Madrid.
Moretto indicated that neither club is likely to welcome the prospect of losing a key midfielder during the season.
Manchester United's interest in the pair comes despite a substantial investment in their midfield during the summer. The club brought in Carlos Baleba, Andrey Santos and Youri Tielemans, but the early-season performances have not removed concerns about the balance of the team.
The recruitment search is not limited to central midfield. According to The Athletic, United are also considering a new left-back to provide cover amid a series of injury problems.
RB Leipzig defender David Raum has emerged as a possible target, with the Germany international reportedly among the options being assessed ahead of January.
The potential interest in Raum reflects another area where United could seek greater depth, particularly with availability issues affecting their defensive options.
There is also uncertainty surrounding the managerial position. Michael Carrick has come under pressure following the team's poor start, leaving questions about the direction of the club's recruitment plans.
For now, the approaches for López and Barrios remain exploratory, while Raum is one of the names linked with the left-back search. United have yet to confirm any formal offers or advanced negotiations for the three players.