Northern Ireland international Healy scored 45 goals for North End between December 2000 and October 2004 when he moved to Leeds in acrimonious circumstances.
The 33-year-old is a free agent after leaving Rangers at the end of last season, but Westley feels his move across the Pennines almost eight years ago and subsequent celebration when scoring against Preston shortly afterwards is reason enough to pull the plug on any deal.
"Making a controversial move, on my part, would be the wrong thing to do," Westley told his club's official website. "I have spoken to David to let him know that we are not going to proceed with that at this moment in time.
"It is a difficult one, because David has so much proven quality, but my feeling is that we've had a revolution at this club this summer.
"It has been a difficult time and the fans have been through a lot. They have been brilliant in getting behind the new team. There is a body of supporters who have a strong feeling against the move and I think it would be the wrong thing to do."