Speaking from Los Angeles, a spokeswoman for the club said United still hoped the 29-year-old would be able to join them once his "personal administrative issue" had been resolved.
British media reported on Monday that Sanchez was understood to have failed to get a US visa due to a 16-month suspended jail sentence imposed by a Spanish court in February for tax fraud.
He was accused of defrauding the Spanish state of a combined 983,000 euros (A$1.5 million) in image rights when playing for Barcelona in 2012 and 2013 by using a shell company in Malta and omitting the earnings from tax returns.
Spanish law is such that any sentence under two years for a non-violent crime rarely requires a defendant without previous convictions to serve jail time.
The BBC reported that Sanchez, who was training with United last week after a summer break without any World Cup action, was working with his lawyers to secure entry to the US under a waiver scheme.
The rest of the squad, without the club's World Cup players, departed on Sunday.
United's opener in their five-match tour is against Mexico's Club America in Los Angeles.
They will also play Major League Soccer side San Jose Earthquakes before taking on AC Milan, Liverpool and Real Madrid in the International Champions Cup (ICC) tournament.
If Sanchez fails to secure entry to the US, United have a friendly at Bayern Munich on August 5 before their league opener against Leicester City at Old Trafford on August 10.