He's about to join Arsenal in a £32 million move, but according to the paper, the Red Devils had the chance to secure his services, only for the Gunners to offer a huge contract that Manchester United weren't willing to match.
They add that the "mega offer", which is believed to be worth around £135,000-per-week also prompted Liverpool to pull out of the race for his services.
The Chile winger, who starred for his country at the World Cup, is expected to complete his move to Arsenal shortly. Manchester United meanwhile will seemingly focus on landing his countryman Arturo Vidal from Juventus.
Manchester United transfer gossip:
Elsewhere Patrice Evra is close to joining Juventus despite recently signing a new deal at Old Trafford.
The Frenchman joined the club from Monaco in 2006 and was expected to stay put and provide cover for Luke Shaw, however he now seems destined to leave (BBC Sport)
Evra's switch to Turin could pave the way for Vidal to join Manchester United, and a £32 million deal is being discussed (The Express)
Manchester United have tabled an offer for Swiss full-back Ricardo Rodriguez with Evra heading for the Old Trafford exit (Daily Mail)
Manchester United could be about to sign a record-breaking £60 million-per-season kit deal with Adidas (The Express)
Angel di Maria is at the top of Louis van Gaal's transfer wishlist this summer (The Guardian)
the Dutchman is also eyeing up a deal for Mats Hummels, and will pay £75 million for the pair (The Guardian)