The Daily Mail says Toon boss Sam Allardyce had said that Smith was not among his targets, but injuries to Joey Barton and Michael Owen in what is an already threadbare squad have caused him to switch his sights to the versatile England man.
Aston Villa and Middlesbrough are also in the hunt for the 26-year-old, who has 18 England caps, but it is believed the player's preferred choice is Everton if they can raise the money.
Smith is keen to return to his more accustomed role as a striker but his ability to play in midfield makes him an attractive option for a stretched Newcastle.