Bolton have been linked with a move for the former England Under-21 international. Birmingham need to generate income after losing their Barclays Premier League status as manager Alex McLeish looks to rebuild his squad.
Bolton have made initial contact with City who will want in excess of £5million for the former Cardiff player.
Stoke were also linked with Jerome during the January transfer window.
He has been the mainstay of the Blues attack for the past five years and scored 11 Premier League goals during the 2009-2010 campaign.
But last season Jerome went 23 games without a top flight goal from November, although McLeish praised his overall contribution to the Carling Cup winners.
McLeish is also preparing himself for possible moves for other members of his squad.
Wolves boss Mick McCarthy is known to be an admirer of Blues central defender Roger Johnson who has also been linked with Blackburn, Bolton and Sunderland.
But no formal offer has yet been received for a player who moved from Cardiff for £5million two years ago.
Source: PA
Source: PA