Allardyce took charge of the Hammers five years ago and led them back into the Premier League via the Championship playoffs at his first attempt, after the Irons were demoted under Avram Grant.
Noble, whose West Ham testimonial happens at Upton Park this afternoon, claims that he had the option to leave the East Londoners that summer, but says that the arrival of the former Bolton Wanderers boss helped make his mind up.
“The question was asked when we got relegated in 2011," the 28-year-old, who has been on the Hammers' books since he was 13, is quoted as saying by The Mirror. “I remember being away on holiday and getting phone calls from my agent, who told me that people had been in touch.
“But when I realised Big Sam Allardyce was coming in, I just batted it all away. I love this club. Sometimes the grass is not always greener on the other side.”
Despite firmly re-estabishing West Ham in the top flight, Allardyce was sacked last summer and replaced by Slaven Bilic in what has proven to be a shrewd move by the club's hierarchy so far.
As it stands, Bilic's side sit fifth in the Premier League table, one point behind fourth-placed Manchester City in the race for Champions League qualification, while an FA Cup quarter-final replay with Manchester United also looms large next month.
It has been a wonderful season for the Croat, though much of his success is down to the players he inherited from Allardyce, like Adrian, Winston Reid, Aaron Cresswell, Cheikh Kouyate and of course Noble himself.