Allardyce revealed back in June that he was initially under consideration to replace Rafael Benitez at St James' Park but says he rejected the chance to return to the role, which he previously held between 2007 and 2008.
"Newcastle wasn't for me," Allardyce told Sky Sports. "I was very chuffed that Mike [Ashley] considered me again but I felt that Brucey was a better fit than me and good luck to him.
"It is his dream move to manage his home town club and I wish him well. It was the only thing that came up this summer."