Blues sources indicate they expect a deal for Davies to be struck in the next 24 hours.
It is likely that the 25-year-old will move from Villa Park to St Andrew's in a straight cash deal worth around £3.5million. But the two clubs are also discussing a possible swap deal involving Blues winger Sebastian Larsson plus a £1.5million cash adjustment in Villa's favour.
Davies had indicated that he was anticipating a return to Leicester for a second loan spell.
But then Blues made their interest known in signing the former England Under-21 player, who has slipped down the pecking order at Villa.
Meanwhile, Blues boss Alex McLeish has made no secret of his desire to sign a striker this month and the latest potential target on his radar is former Newcastle forward Obafemi Martins.
He made the switch from Wolfsburg to Russian side Rubin Kazan during the summer.
McLeish is keen to bring in someone who could instantly adapt to the Premier League and Martins would fit the bill after his spell at St James' Park.
But the Blues boss would only say: "The board are trying very hard to bring someone in and are working around the clock in terms of negotiating with people.
"After a couple of disappointments (Robbie Keane and Kenny Miller) I prefer not to discuss anyone publicly until the i's have been dotted and the t's crossed in any deal."