Bale is renowned as one of the hottest young properties in world football after starring for Tottenham over the last two seasons.
He grabbed the world's attention when he ran Inter Milan ragged on two occasions last season and his reputation has improved this term thanks to a number of impressive displays.
Barcelona have watched the 22-year-old on a number of occasions and this week Barca full-back Dani Alves said Bale would be a welcome addition to the ranks of the all-conquering European champions.
Redknapp insists there has been no approach for Bale yet though, and claims the wide man is content at White Hart Lane.
Redknapp told a press conference: "No one has been in touch with us.
"He is happy here with us at the moment. He is a fantastic player.
"He will be linked with every club because he is such a great player."
Barcelona's players were heavily criticised last year for talking publicly about their desire to see then Arsenal captain Cesc Fabregas return to the Nou Camp - a tactic many saw as tapping up.
When asked whether he thought Alves' comments constituted tapping up, Redknapp replied: "I haven't seen what he said.
"I would like Lionel Messi. I will have a chat with the chairman about Lionel. I will see if he fancies coming to Tottenham!"
Barcelona suffered a shock 1-0 defeat to Chelsea on Wednesday night in their Champions League semi-final first leg clash at Stamford Bridge.
Should Chelsea win the Champions League, Spurs will be denied a place in the competition if they finish fourth in the Barclays Premier League, but Redknapp claims he still wants the Blues to go through following Tuesday's second leg in Spain.
He added: "I'll be rooting for Chelsea. I haven't even thought about [missing out on the Champions League if Chelsea win the whole thing].
"If Chelsea stay in it, they've got a Champions League Final to prepare for as well and that'll mean they've got a lot on their plate and I want to see an English team win it anyway."