Dann has played 60 games since joining Birmingham from Coventry
Stoke have had a joint bid of about £10m rejected by Birmingham for defender Scott Dann and striker Cameron Jerome, BBC Radio Stoke understands.
It is thought the Potters are not willing to increase their offer for the pair, who they were initially reported to have bid £16m for.
Dann, 24, who moved to St Andrews from Coventry for £3.5m in 2009, has also been linked with a move to Liverpool.
Jerome, also 24, rejected a move to the Britannia Stadium in January.
At that time, Potters chairman Peter Coates said: “Jerome is a player we like and something might happen.”
The former Middlesbrough trainee has scored 41 goals in 200 appearances since joining Birmingham from Cardiff in May 2006.
He was Birmingham’s top scorer in the 2009/10 Premier League season with 11 league goals, but last season scored just five in total as the Blues were relegated to the Championship.
His last league goal came against Stoke in a 3-2 away defeat on 9 November 2010.
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Jerome’s last Premier League goal was in Birmingham’s 3-2 defeat at Stoke in November
A hamstring injury forced Dann to miss the final four months of last season.
In the previous campaign, the impressive defensive partnership he forged with Roger Johnson helped the Blues finish ninth – their highest league finish in 51 years.
Dann and Jerome could follow Craig Gardner out of St Andrews, with the midfielder poised for a move to Sunderland.
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Stoke fail in Birmingham duo bid