The Red Devils have decided that the Premier League pair are too expensive with Leicester City and Tottenham thought to be demanding £75million for their defenders.
That would represent a joint-world record fee, alongside the money that Liverpool spent on Virgil van Dijk in January, for a centre-back.
But the position remains an area in which Jose Mourinho desperately hopes to improve before next Thursday’s transfer window deadline (5pm).
And as such, according to Goal, United have decided to move away from their first and second targets to the cheaper alternative of Mina – who has been linked to several Premier League clubs this summer.
Everton are also keen on the Colombian international, who scored three goals at the World Cup, having already snapped up left-back Lucas Digne from Barcelona this week while West Ham, Wolves and Leicester are among the other clubs linked.
Goal say that the towering 23-year-old would set United back less than half of what they would need to pay to land Maguire or Alderweireld with a €40m (£36m) price-tag mooted.
That’s despite having only made six appearances for Barca since joining from Brazilian club Palmeiras in January having struggled to displace Gerard Pique or Samuel Umtiti in Ernesto Valverde’s starting eleven in his short stint at the Nou Camp.
Yet it is claimed that Mourinho has been impressed enough in Mina’s quality to green light a move, with the only hold-up in any deal being Barca’s insistence for a buy-back clause.
United are keen to sign Mina without any such stipulation included although Barca are keen to negotiate one, having re-signed Gerard Deulofeu from Everton a year ago through such means.
And Goal do not believe the clause to be any major issue, insisting that an agreement is close to make Mina United’s fourth summer signing.
Mourinho has already welcomed Fred, Diogo Dalot and Lee Grant to Old Trafford.
But the Portuguese boss has eyed further additions to strengthen his squad as they look challenge rivals Manchester City for the league title, having finished 19 points adrift of the champions last term.
The United boss has been vocal in his frustrations at a failure to sign more players although he has hinted that United would secure his top transfer priority of a new centre half.
Speaking to BeIN Sports recently, Mourinho said: “I’m confident I’ll get one [more signing].
“I think two is not what I will get. I think in every pre-season it happens basically the same with probably every club, which the manager wants more. It is our nature and our way to always want more for your team.
“But club decisions are different. Normally you don’t get what you want which basically happened throughout my career. If I sign one player before the window closes, that’s fine.”
United round off their pre-season campaign with a trip to Bavaria to face Bundesliga champions Bayern Munich in a standalone friendly on Sunday (7.15pm).
Mourinho’s men then kickstart their top-flight campaign against Maguire’s Leicester next Friday (8pm).