During his three-year spell in charge, the Spaniard guided Boro to the Premier League, but after a winless run of 10 games his exit was mutually decided.
Redknapp's last job in club management was in 2015 when he coached Queens Park Rangers, but it does not seem that he will return to the dugout at Middlesbrough.
When asked on talkSPORT if the job could be his, Redknapp said: "No chance. I'm not even in the running. Not a prayer."
Steve Agnew is in temporary charge of the Boro team.