Albion deny Ridgewell reports
Both clubs confirmed last week that an initial offer for Ridgewell, who can play at left-back and centre-half, had been rejected.
But sources close to the Baggies - as well as Blues - are adamant a fresh, improved offer has not been lodged.
Albion insist the club's stance has not altered from head coach Roy Hodgson's media conference on Friday when it was indicated they would "move on" from attempting to sign Ridgewell.
The 27-year-old stressed his desire to leave St Andrew's last summer amid interest from Premier League clubs. City, however, turned down a transfer request from the versatile defender which came within 24 hours of the close of the window.
Ridgewell had previously been linked with moves to Everton, QPR and Newcastle following Birmingham's relegation last season.