The Magpies had approached the Bantams for permission to talk to the 58-year-old about becoming Alan Pardew's deputy at St James's Park but former England Under-21 manager Taylor has declined to take up the position.
Taylor told the city's official website: "I was flattered to be asked by Alan Pardew to be his assistant at such a huge club like Newcastle United. It is something I have always said I would be interested in one day.
"I have a lot of respect for Alan and for Newcastle United, who are a magnificent club, but I just really didn't want to break my commitment here at Bradford. At present, I am contracted here until the end of the season and I didn't want to walk away from that any earlier.
"I believe in what we are trying to achieve here. We have started the new year in a good vein of form and it's up to us to keep that going. I would like to wish Alan and Newcastle all the very best for the remainder of the season, but now we must focus on ourselves."