But boss Redknapp feels selling the 21-year-old could generate a steady decline at White Hart Lane.
"We couldn't look to sell him," said Redknapp in the London Evening Standard.
"You start selling him and it sends out the wrong signals. For me it would be like when West Ham sold Rio at that time.
"They think, 'Well, the club's not got any real ambition, we're not going anywhere', and I think that would happen with Gareth.
"We've got to keep him here as long as we possibly can and really build the team around him. It's those people you've got to keep."