Pardew has been working without a number two after succeeding Chris Hughton at St James' Park last month and had earmarked the experienced Taylor for the role.
However, the former England Under-21 boss has opted to remain at Bradford.
Lawn told the Yorkshire Post: "Newcastle approached us between Christmas and New Year and we subsequently agreed compensation for the remainder of Peter's contract.
"But since then Peter has indicated he wants to stay and we hope that is the end of it."
Bradford are 10th in npower League Two and beat Bury 1-0 yesterday.