Harry Maguire, who could face United for Leicester on Friday, Bayern Munich's Jerome Boateng, Toby Alderweireld of Tottenham and Mina were all linked with United, while Atletico Madrid's Diego Godin emerged as a late target on Thursday.
Yerry Mina was offered by Barcelona to United and a number of other clubs before the World Cup for €11m in an attempt by the Spanish champions to get their money back on a player they signed in January.
He said: 'Manchester United have to go out with the intention of winning everything that's put before them.
The Old Trafford faithful had demanded the club make a strong statement after United finished 19 points off the top of the Premier League a year ago.
A new season begins tomorrow with Manchester United looking to catch up to neighbours City.
Although they are in the market for a centre-back, the Red Devils now appear to have withdrawn from the race.
The centre-back discussion has only become an issue this summer, and the club have felt that the options open to them have not warranted the investment they would have required.
But an inconsistent defense may get a test from England worldwide striker Jamie Vardy, though the Foxes did lose their best player - Riyad Mahrez - in the summer as he was sold to Manchester City.
Tottenham boss Mauricio Pochettino has been one of the more outspoken critics of the shortened window with time running out for Spurs to make a single signing this summer.
Jose Mourinho confirmed that as many as 10 players are likely to miss the Premier League opener.
"I'm astonished that a club of their ilk, a club who with their clout, a club that finished so far off the pace previous year in terms of the points gap - we know they finished second but the points gap was huge - that they have done little or nothing", Burley said.
"I do not trust that new players will arrive and I'm not confident in that so now I will only focus on the players I have", he said.
"But again, the perception of the people that reads can be different, but I like my players and my group".
"But it's the same conversation as with (Ashley) Young, (Marouane) Fellaini, (Jesse) Lingard, it's the same".
"So, when you repeat 1,000 times that my relationship with my players is not good, it's a lie that repeated 1,000 times is still a lie".