Dudek, whose contract at Liverpool runs out this summer, revealed on Thursday that he was considering an offer from Madrid, where he would provide competition to Spain number one Casillas.
And Casillas admits he would be delighted to have the hero of Liverpool's penalty shoot-out win in the 2005 Champions League final - who at 34 is eight years Casillas' senior - on board at the Bernabeu.
"It would be a pleasure to have such a good keeper come here. We will work hard side by side if the signing is confirmed," said Casillas.
Dudek has been forced to play second-fiddle to another Spaniard, Jose Reina, at Anfield for the last few years and has made only a handful of appearances for the Reds since the victorious Champions League final against AC Milan two years ago.