The City skipper has struggled this season with injuries and his team-mates have missed the centre-back, struggling to win in his absence.
Since his move to Eastlands in 2008 the Belgian defender has proved integral to the club's success, captaining the Citizens to their first Premier League trophy.
And his importance to the side was highlighted again yesterday when a Kompany-less City slumped to a late defeat against Chelsea at Stamford Bridge.
Chelsea's winner came in the last seconds, following a defensive mix-up between Matija Nastasic and 'keeper Joe Hart.
The young defender, though partly at fault for the goal, has proved himself a good prospect for the future.
However, Mancini doesn't rate Joleon Lescott, whilst Javi Garcia looks uncomfortable at the back.
The club brought in Martin Demichelis in the summer, but the Argentinian will take time to adapt to the league.
And former hero Corrigan believes the club need to invest in another top-class central defender.
“Manchester City did go out and buy a centre-half [Martin Demichelis] in the close season," Corrigan said on talkSPORT. "But it seems when Vincent Kompany is out of the team the confidence of the back four suffers. In a top squad that shouldn’t be happening.
“You should have more than one general in charge of it all. When Vincent is out of the team they do struggle, especially away from home.”
The defeat leaves City in seventh, six points away from leaders Arsenal, while Chelsea move within two points of the Gunners.
It was hoped Kompany would be fit for the Stamford Bridge clash, and after missing out, City chiefs will be hoping they can get their centre-back fit as soon as possible.
Next up for Manuel Pellegrini's side is an away game in the League Cup against Newcastle United.