Jones is thigh high after injury reprieve.
The Trinidad & Tobago striker went off at half-time in the Black Cats' 1-1 draw with Man City at the weekend, after heading the Wearsiders in front.
And immediately after the game boss Steve Bruce feared that he would be without his eight-goal second top-scorer for a month or more.
But tests have shown that Jones has merely strained his hip flexor muscle, and he is likely to be in contention when the Blues visit the Stadium of Light this weekend.
Bruce will not make a final decision on his fitness until tomorrow, but on-loan Man City frontman Benjani is on standby to make his first start for Sunderland and partner Darren Bent if Jones is not ready.
Bruce said: "It's a lot less serious than we first thought, and there is a chance Kenwyne could be fit this weekend.
"We'll see how he is tomorrow. "Kenwyne has been playing well of late but, at least if he is out, we have got Benjani to come in and take his place."
While Jones could yet figure against Birmingham, the chances of Sunderland's midfield driving force Lee Cattermole returning to fitness this weekend seem remote.
Bruce admitted that the former Wigan and Middlesbrough man is 'still struggling' with a hamstring problem.
And with skipper Lorik Cana completing a two-match ban, Bruce is set to stick with the central midfield partnership of Kieran Richardson and youngster David Meyler that did so well against City. Meyler in particular was outstanding against City's bigmoney stars - and all the more so considering it was only his third Premier League start.
Bruce said: "It's still a bit of a struggle for Lee and of course Lorik is unavailable.
"But young David Meyler came in and played very well against Man City. "One thing he has got is a huge heart and a huge appetite for the game.
"He's only 20 but he came in and the stats showed he ran 13km last Saturday. "It would be very difficult for me to leave him out of the team - he's put a huge marker down for himself and now he has to live up to that level."