The Bluebirds have told Birmingham to pay £5million up front for Johnson or forget about a deal.
The Welsh club have angrily rejected a "hire purchase" offer for the 26-year-old defender.
The deal would see Cardiff get £1m a year over four years with another £250,000 a season for every year Birmingham stay in the Premier League.
A Cardiff insider told The Sun: "The bosses here think the Birmingham offer is rubbish. Johnson will stay if that's the best Birmingham can do.
"Our fans would see a headline figure of £5m and expect us to spend that on replacements. Who knows whether Birmingham will stay up?"