The Daily Star says Kompany has been left devastated following his latest injury blow which has seen him ruled out for four weeks.
He suffered a quadricep problem - near to his troublesome groin - during Saturday's 3-1 win over Everton.
It is the Belgian ace's second significant injury of the season and scans yesterday revealed the seriousness of the damage. Kompany is out of his country's World Cup double header and will be further assessed in a week.
City bosses were already worried about Kompany's long-term fitness but the latest setback has put them on red alert.
A club source revealed: "The injuries are piling up and it is looking like only a matter of time before he flies out to consult a specialist.
"His long-term health and fitness have been a big concern for some time now, dating back as far as the end of last season, which was very much an injury-hit campaign for Vincent.
"The feeling now is that he is at a point where it is difficult to avoid muscle injuries for more than a month or so.
"This causes untold disruption, not only to the team's confidence and preparation but also to the player's body.
"When he is playing he is striving for match sharpness. Players need continuity, but these injuries are interrupting his flow.
"He hurt his upper groin and that area in particular is really susceptible for Vincent.
"As you would expect, he shares everyone's frustration."
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