The Polish stopper is behind Jose Reina and Scott Carson at Anfield and is desperate to quit for
first-team football.
Black Cats boss and chairman Quinn is hoping Dudek is prepared to step down to England's second tier to take part in Sunderland's bid for promotion from the Championship.
That bid got off to a poor start after a 2-1 defeat by Coventry on Sunday, and Quinn wants a more experienced keeper having had to field Ben Alnwick in goal following the sale of Kelvin Davis to Southampton.
Quinn has already shown his ambition in the transfer market having been thwarted in a bid to land Spurs duo Calum Davenport and Andy Reid.