Amos has not played for Bolton for the last two years having spent loan spells at Cardiff City and Charlton Athletic during the last two seasons.
The former Manchester United keeper impressed during his loan stint at Charlton, making 50 appearances in all competitions and keeping 14 clean sheets.
The 28-year-old's future at Bolton remains up in the air with the club willing to listen to offers for Amos so that they can trim their squad and reduce their wage bill.
Birmingham are scouring the transfer market for goalkeeping reinforcements this summer after Blues boss Garry Monk informed David Stockdale and Tomasz Kuszczak that they are not part of his plans going forward at St Andrew’s.
Birmingham have bid for Ipswich goalkeeper Bartosz Bialkowski, but they could turn their attentions to Amos if Ipswich refuse to sell the Polish international.
Millwall boss Neil Harris is also looking to strengthen his goalkeeping options ahead of next season as he looks to provide cover and competition for current No.1 Jordan Archer and Amos is on his list of targets.