Cole, 31, completed his move from Liverpool to Upton Park on Friday morning, signing an 18-month contract with Sam Allardyce’s side.
The former England international midfielder broke onto the Premier League scene at West Ham under Redknapp, who handed him his debut in the top flight, aged just 17, after spending four years at the club’s youth academy.
And Cole had the chance to reunite with Redknapp at a struggling QPR side during this January transfer window, but while he admits he owes a lot to Redknapp, he says he could not resist the opportunity to return to his boyhood club.
“That was the hardest thing for me,” Cole explained to London 24, “because Harry gave me my first chance and I will be forever indebted to him, but there was too much here at West Ham for me to say no.
“The only hard thing was turning down Harry because I love him and I would not be the player I was if it wasn’t for him.”
Hammers boss Sam Allardyce feels the former Chelsea man can now push on at Upton Park and force his way back into the England set-up.
But Cole, who has 56 caps for his country, is concentrating on regaining form for West Ham first.
“I need to get playing first, and probably will need three or four matches to get back to top level,” he said.
“I will always harbour those ambitions because I love playing for my country, but it will be down to performance.”