United are facing a race against the clock to sign a new central defender before Thursday's transfer deadline.
The 23-year-old struggled during the second half of last season, but scored three times for Colombia during an impressive 2018 World Cup, which has led to a host of speculation surrounding his future.
Last week, it was reported that United had already agreed personal terms with Mina over a move to Old Trafford, and according to The Sun, the Red Devils have now made an offer to Barcelona of £35m.
United are believed to have rejected a players-plus-cash offer from Barcelona for Paul Pogba, with Mina and Andre Gomes the two said to be a part of the bid. However, Jose Mourinho's side are still believed to be keen to tie up a deal for the central defender.