Ever since Kompany limped off against Newcastle United, City have been trying to figure out what to do about it.
Manchester City's roster is a decadent frosted doughnut. Everything is sweet except the hole in the middle of the defence.
If City did not have bad luck with centre-backs these days, they would have no luck at all.
It was easy enough to shrug off Matija Nastasic's ankle injury as a fluke that can happen when a team decides to play so many starters in a July exhibition match played on a waterlogged pitch half a world away.
But then City lost captain Vincent Kompany to a groin strain against Newcastle United in the Sky Blues' Premier League opener, which sadly subjected City to the comedic stylings of Javi Garcia on the back line.
Now might be a good time for Manuel Pellegrini to consider tabbing another player as an emergency centre-back. While removing Yaya Toure from the midfield diminishes it, he would have to be an upgrade over Garcia on the back line.
(Though at least when Garcia is subpar as a defender, he has an excuse. No one has offered a reasonable explanation for his comparably shoddy efforts in the midfield.)
Nastasic's return against Hull City was welcome, though the pairing with Joleon Lescott did not exactly inspire unshakable confidence, not with Lescott and Nastasic muffing a clearance and sending Sone Aluko in on Joe Hart.
City and Hart, both suffering from confidence crises as the match started, could have done without that particular gaffe so early in the match.
Smartly, then, City made sure to patch the hole in front of Hart by signing Martin Demichelis from Atletico Madrid as the summer transfer period was ending.
That worked out great right up to the point where Demichelis injured himself in training and is now projected to miss six weeks, per ESPNFC.com.
City are probably not going to develop a need for any more midfield help between now and January.
Even with Gareth Barry going to Everton, City still could roll out Samir Nasri, Jack Rodwell, Garcia and James Milner in midfield. Those four players, all reserves for City, would start for most Premier League sides.
Similarly, though I would not be averse to seeing City take another run at Stephan El Shaarawy, they have four very good strikers and look unlikely to need a fifth attacker in January.
And despite Jesus Navas' recent not-very-helpful chatter about Iker Casillas, Hart is still only 16 months removed from a Premier League title and, at 26 years old, in what should be the prime of his career. There may come a time where Pellegrini pulls the plug on Hart, but it should not be as soon as this January.
City might aver that by the time January rolls around, the starting back line of Pablo Zabaleta/Nastasic/Kompany/Gael Clichy will be fully healthy and so more back-line help will not be needed. For that matter, Micah Richards and Demichelis should also be fit.
But if Kompany's recent absence has driven home anything for City, it is that every central defender they have behind Kompany (even Nastastic, regrettably) is a real step down from the captain.
As such, if City progress past the group stage in the Champions League and/or are in contention for the Premier League title in January, their financial clout should go to signing another top drawer centre-back.
Which brings us back to Pepe.
City had the veteran Real Madrid defender in their sights for much of the summer. Ultimately, Real Madrid decided not to part with Pepe before the recent window closed.
If, as Richard Jolly reported for ESPNFC.com in August, City's "hopes of signing Pepe could rest on whether Real Madrid bring in Gareth Bale," it might be worth City's while to sound the Spanish club out now that that shoe has dropped.
Whether it is Pepe or another veteran centre-back, that position is the one City must (again) address in the coming transfer window.
Faking it at centre-back with the likes of Garcia and even Demichelis is just not the sort of thing a Champions League contender does.