Spanish newspaper Marca suggested on Friday that Tottenham had sanctioned Bale's departure to the current European champions for a fee of €40 million.
Bale admitted last month that he would review his future if Spurs failed to qualify for the Champions League, and Barca defender Dani Alves said in a recent interview that the Welshman would fit in well at the Camp Nou.
Redknapp insists the 22-year-old is not leaving White Hart Lane this summer, however. The Spurs boss said: "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.''
Redknapp, who fought off interest from Chelsea to keep Luka Modric at Spurs last summer, insists the club will not lose their best players if they do not qualify for the Champions League.
"That idea gets a bit over-hyped,'' said the 65-year-old, whose team host Fulham on Sunday in the last game of the season.
"When Gareth came to Tottenham, they weren't in the Champions League. When Luka Modric came here, they were nowhere near.
"He didn't come here because they were in the Champions League, he came here because they were a good club, on decent money and had a chance to play in the Premier League.
"Are you telling me people aren't going to sign for Chelsea next year if they don't win the Champions League this year because they won't make it next year? Of course they'll sign for Chelsea, if they are paid the right money and get the right contract, they are going to a fantastic club in London.
"They will still go to Chelsea. They will go to Liverpool because it is a great club and they will still come to Tottenham because it's a great club.''
Bale signed for Tottenham from Southampton in 2007 for an initial fee of £5 million and has since emerged as a vital player for the North London club, scoring 21 goals in 112 Premier League matches.