Earlier this week, Barcelona defender Dani Alves said that Bale would be a welcome arrival at the Camp Nou.
Spurs are in danger of missing out on Champions League football next season, leading to speculation Bale may have his head turned if he misses out on parading his talents on the biggest stage, but Redknapp was bullish when questioned on the Barcelona link.
"No one has been in touch with us," Redknapp said. "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.''
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!''