Black Cats manager Steve Bruce tried to sign Crouch two summers ago from Portsmouth but the 30-year-old opted to move to White Hart Lane instead. The towering striker enjoyed a successful first season in north London but struggled slightly last term, with just four of his 11 goals coming in the Barclays Premier League.
When asked whether Crouch would leave Tottenham this summer, Redknapp told the BBC: "I doubt it. Crouchy is a good player. I like him. He is a great lad and I love him as a fella."
Redknapp added: "He is not one I'm looking to shift. We are looking to bring a striker in but he is not one of those that we are looking to sell if we can help it."
Crouch himself made it clear earlier this week that he does not want to leave the club.
One striker who is expected to depart is Robbie Keane, who is back at his parent club after West Ham's relegation saw a potential ?£6million deal fall through.
Fulham, now under the stewardship of former Spurs boss Martin Jol, could make a move for the 30-year-old, who was a regular under the Dutchman during his time at White Hart Lane.
Source: PA
Source: PA