"We are talking with Birmingham after we were told we could do so by Cardiff. So from that you can presume they have agreed terms," Jeromes agent, Tony Finnigan, told skysports.com.
"At this moment they are the only club we are talking with or have been told we can talk with.
"We would expect Cameron's future to be decided by early next week."
Baggies boss Bryan Robson is also keen on signing the England Under-21 international but he recently had a swap deal bid involving Jason Koumas rejected by Cardiff.