Spanish newspaper Marca suggested on Friday morning that Spurs had sanctioned Bale's departure to the current European champions for a fee of 40 million euros.
Bale admitted last month that he would not be able to turn down a move to the Catalan giants and Barca defender Dani Alves said in a recent interview that the Welshman would fit in well at Camp Nou.
Redknapp insists the 22-year-old is not leaving White Hart Lane this summer, however.
The Spurs boss told a press conference: "I don't know anything about [the story linking Bale with Barcelona]. I wouldn't think there is the slightest bit of truth in that. Not a chance, I wouldn't have thought."
Bale shot to prominence with a series of stunning displays in the Champions League last season and has caught the eye again for Spurs this term.