The Baggies are understood to be considering an offer from City with just two days remaining until the transfer window closes. Bednar recently returned to the Baggies after a loan spell with Leicester.
The former Hearts player indicated he was willing to fight for a first-team place, but the arrival of Arsenal striker Carlos Vela on loan for the rest of the season has pushed Bednar further down the pecking order.
Leading scorer Peter Odemwingie and Marc-Antoine Fortune are already ahead of Bednar in the battle for a starting spot at the Hawthorns while Vela is set to make his debut in Tuesday's home Barclays Premier League clash with fellow strugglers Wigan.
SV Hamburg striker Eric Maxim Choupo-Moting is also still on the Baggies' radar as the transfer window enters its final two days. But Albion head coach Roberto Di Matteo insisted: "I've always said I won't do anything for the sake of it and that remains the case."