The crocked midfielder is not due back at the team's training ground until September 23 after having surgery on both knees to cure a career-threatening tendinitis problem.
United play their Group B opener against Besiktas in Turkey eight days earlier.
In theory, Hargreaves, 28, could be fit for the Old Trafford clash with German champs Wolfsburg on September 30.
But it is more likely the ex-Bayern Munich star will return to action for the ties with CSKA Moscow in October and November.
Hargreaves joined United for £17million in 2007 and has not played since the 1-1 draw with Chelsea on September 21 last year.
Manchester United have been named the world's most valuable sports club by Forbes Magazine.
Their total value is put at £1.17billion, £200m more than gridiron's Dallas Cowboys.