Bialkowski was one of the few Ipswich players to emerge with any credit in a campaign that saw the East Anglian side relegated from the Championship.
And he could make an instant return to the second tier, with Birmingham already identified as a possible destination.
But the Blues appear to face competition from one of their divisional rivals, Millwall.
Millwall are desperate for goalkeeping reinforcements, having allowed Jordan Archer and Ben Amos to leave at the end of their deals, and seen David Martin lured to West Ham.
Bialkowski is unlikely to come cheap, however, with his Ipswich contract running for another two seasons.
It is just 18 months since the 31-year-old, who has been capped once by Poland, was linked with a £4 million move to Crystal Palace, also by The Daily Mirror.
Will Millwall, Birmingham or someone else win the race to sign the Ipswich 'keeper?
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