The England international was apparently hoping for some time on the pitch in order to press his claims for a place in Fabio Capello's squad for this summer's World Cup in South Africa.
However, the report claims that the star left Old Trafford at 3.10pm in his grey Audi on Sunday afternoon in something of a rush.
The official reason given by United for his departure was illness.
Hargreaves was omitted from England's provisional 30-man squad for the World Cup on Tuesday, with Capello opting instead to include Manchester City's Gareth Barry, who is currently sidelined with an ankle injury.
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