Dann is widely expected to leave St Andrew's during the transfer window in the wake of the Blues' relegation from the top-flight on the final day of last season.
The imposing centre-back formed an impressive partnership with Roger Johnson before an untimely injury in January curtailed his campaign and contributed to the club's eventual demotion.
Gunners boss Arsene Wenger is known to be keen to strengthen his defence having seen their hopes of silverware undermined last season by deficiencies at the back.
And the Emirates Stadium outfit have held initial discussions with the St Andrew's club over bringing the 24-year-old to North London.
A host of Premier League clubs, including Chelsea, Liverpool, Aston Villa and Stoke have all been linked with the former Walsall and Coventry man this summer.
But it now appears that Arsenal have jumped to the head of the queue for the player who moved to Birmingham in a £3.5million deal in the summer of 2009.
Wenger is likely to have funds to invest in the transfer market with captain Cesc Fabregas expected to complete his multi-million pound return to Barcelona in the coming days.