Black Cats manager Steve Bruce is looking to add new faces to his squad with the ?16million he is set to receive from Jordan Henderson's expected transfer to Liverpool.
Bruce tried to sign Crouch - who is on holiday in Sardinia with his wife Abbey Clancy - two summers ago from Portsmouth but the 30-year-old opted to move to White Hart Lane instead.
Not for sale: Tottenham do not Peter Crouch, who is on holiday with his wife Abbey Clancy and his daughter in Sardinia, to leave White Hart Lane
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.
The poor form of Jermain Defoe and Roman Pavlyuchenko has also left Redknapp in no doubt that he needs a new striker, and Didier Drogba, Leandro Damiao and Mousa Dembele have all being linked with the club.
That does not mean Crouch's days at White Hart Lane are numbered though, the Spurs boss insisted.
Not heading off: Harry Redknapp has told Sunderland that Crouch is not going anywhere if he can help it
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.
'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.
On his way: Spurs will look to sell Ireland striker Robbie Keane this summer with Fulham interested
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.
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Explore more:People: Steve Bruce, Robbie Keane, Roman Pavlyuchenko, Peter Crouch, Harry Redknapp, Didier Drogba, Abbey Clancy, Martin Jol, Jermain Defoe Places: Liverpool, London