But despite the club's financial problems, manager Kevin Blackwell wants veteran midfielder Speed in part-exchange plus cash for Milner.
Speed began his career at Leeds and he could be tempted by the chance to make a return to West Yorkshire.
But reports suggest that the Welshman wants to stay at St James' Park because he still believes he can play for at least one more season in the Premiership.
If Newcastle boss Sir Bobby Robson agrees, he will be reluctant to let the 34-year-old leave as he would have to look to the transfer market for a new midfielder if he was to go.