The 29-year-old striker had recently claimed Spurs were a smaller club than his current side Sevilla, but Fabiano appears to have had a change of heart after failing to attract bids from AC Milan and Manchester United.
"I must admit it's only in the last few weeks I have understood just how big Spurs' ambition is," Fabiano told ESPN.
"Yes, I like him. He's a fabulous player and would be a brilliant addition to any team," Redknapp revealed. "It was put to us that he might be available, but we've not made contact with his club Sevilla."
Fabiano has been Redknapp's number one target for the majority of the summer as the Spurs supremo looks to rejuvenate his front-line with world-class strikers for their debut in the Champions League this season.
"I am not unhappy with the squad I have, but of course if a special player came along I would look at it, and Fabiano is a special player all right," he added.
"For sure, he is a class act, but I don't know what he earns. He might be on mega money, so it might prove to be impossible for us."
Transfer speculation has recently linked Spurs with moves for AC Milan forward Klass-Jan Huntelaar, Manchester City's out-of-favour Craig Bellamy, Nice's sought-after Loic Remy and Ipswich youngster Connor Wickham.
