But United have been stunned by Leicester's £75 million of the England global, who still has four years remaining on his current contract.
The Colombia worldwide has already received an offer from Everton but United have asked the defender to delay his decision.
The Colombian worldwide has now fuelled speculation he could be heading to Old Trafford after removing "Barcelona" from his bio on Instagram while he also started to follow Manchester United, Paul Pogba and Antonio Valencia on the social media site.
Mina arrived from Palmeiras in January but the Colombia worldwide defender has struggled to establish himself at LaLiga champions Barca amid links to Everton and Manchester United.
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He has been heavily linked with leaving Barcelona this summer, despite only moving to the Nou Camp in January after unsurprisingly failing to dislodge first choice centre-back pairing Gerard Pique and Samuel Umtiti.
Mina is contracted to Barcelona until 2023 but could be sold while his stock is high after the World Cup.
Earlier this month, Mina admitted that he was unhappy at Barcelona last season and was keen to leave in order to secure more playing time.
"And I was like, 'What, I'm paying for these guys to go shopping!' I had to laugh but the truth is those monsters put the ball where they want, they are great people as well as magicians".
"I thought a lot of things, a lot of bad things", said Mina.
"For me, I understand that there are spectacular players [in his position] but I just wanted to have a minute to impress and it didn't happen".