The influential defender suffered a groin injury in the season-opening Barclays Premier League win over Newcastle last week.
Manager Manuel Pellegrini has said he expects the Belgian to be out for about a month, making him doubtful for the visit of United on September 22.
But the 27-year-old remains optimistic of a quick comeback. While he would certainly appear to have little chance of playing in Belgium's World Cup qualifier in Scotland a week on Friday, he has not ruled out a return soon after.
Kompany told the club's website, www.mcfc.co.uk: "I'll be out for a little while but not too long.
"I may miss the internationals but I hope to be back after that.
"I've been here before and I'm going to work hard to get back as quickly as possible.
"There are worse things that can happen but the only disappointment is that the season began so positively for me and everything went really well during pre-season.
"There is a protocol to follow with any injury and there is a timescale that goes with that.
"If I follow that schedule, I know when I'll be back in a certain amount of weeks and possibly sooner."
That suggests Kompany may not have even ruled out the possibility of playing at Stoke on September 14 or returning for the start of the Champions League campaign a few days later.
He was missed as City suffered a shock loss to promoted Cardiff last weekend.
His importance to the team was also evident during a two-month absence in the second half of last season when City's title aspirations were badly damaged.
But Kompany has dismissed concerns over his long-term fitness.
He said: "It is a freak injury that has nothing to do with the previous problems - it can happen - but I know when I return I'll be absolutely fine."
City's defensive options have been limited at the start of the season by injuries to Kompany, Matija Nastasic and Micah Richards.
There has been renewed speculation City could sign another defender before next week's transfer deadline, with Atletico Madrid's Martin Demichelis strongly linked.
Kompany admits he would not be surprised if a signing was made.
He said: "Maybe we will. I haven't kept in touch with any speculation so I'm not sure but with a few days to go I'm sure it is a possibility as it is at any club of this size."
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- Barclays Premier League