Chelsea have flatly rejected the idea of selling Mata to a Premier League rival. But sources in Spain insist United have already spoken to Mata's agent and could tempt Chelsea's resolve with a £27m offer.
But any move for Mata looks doomed unless a deal could be agreed to send Wayne Rooney in the opposite direction.
And that is something boss David Moyes has so far refused to contemplate, despite Rooney having struggled with injuries this season.
The striker is currently in Egypt on a warm-weather break to recuperate from his ongoing groin problem.
Mata, meanwhile, wants out of Chelsea as he fears for his World Cup place because of his lack of playing time.
His representatives have also been in contact with Real Madrid, Atletico Madrid and Barcelona. It is thought Chelsea would prefer to sell to Atletico - but the ultimate decision rests with Mata.
Moyes was also in Italy to watch Juventus and Chile star Vidal in action against Cagliari.
The 26-year-old recently signed a new contract to stay at Juve until 2017, but that has not put United off.
The Premier League champions are also close to agreeing a loan deal for Real Madrid left-back Fabio Coentrao.