Kompany is facing another month on the sidelines after suffering a reaction on his return from injury against Sunderland on Boxing Day.
The Belgian's current lay-off is his 12th for a calf injury since the start of the title-winning 2011-12 campaign and his third this season.
He has also missed games because of hamstring and groin injuries in recent years and City's medical department want to analyse the problems deeper.
Manager Manuel Pellegrini said: "We are trying to do all (we can) to know how we can help Vincent to try to be fit and not to continue with the same calf problems
So, everything the club can do, we are going to do it."
Kompany's influence on the City side is huge and the team need him fit to bolster their Barclays Premier League title bid in the second half of the season.
In the nine Premier League games in which he has featured this term, City have kept seven clean sheets and not lost
City have lost five of the 10 games he has missed and conceded in nine of them.
Despite that, and concerns Kompany may suffer further problems, Pellegrini has no intention of bringing in extra defensive cover in the January transfer window.
The Chilean said: "No, really I think the squad is complete
As always, I said that we are not going to close the window but we are not really thinking of any special players to bring in."
In terms of positive injury news, midfielder Fabian Delph and left-back Gael Clichy are both back in contention for Saturday's trip to Watford after missing Tuesday's goalless draw at Leicester.
Pellegrini, speaking at his press conference to preview the game, said: "Fabian Delph and Clichy have worked normally
They had some small problems in the last game."
Pellegrini has given his squad permission to enjoy their New Year celebrations - but warned them not to stay up too late.
Asked if his players faced an early curfew, Pellegrini said: "No, not before midnight
All of them must celebrate New Year's Eve but I think they can do it early - maximum one o'clock."
Source : PA
Source: PA