Spanish sports newspaper 'Marca' is reporting that the Welshman has already agreed a deal in principle to stay at the Champions League winners until 2021.
Madrid have had a quiet transfer window, but are hoping that the renewal of Bale's contract will make up for a lack of transfer activity.
Zidane's side are also hoping that Cristiano Ronaldo and Martin Odegaard will sign new contracts in the near future.
Bale is currently the second highest earner at the club and want to offer the winger a deal of around €11m per year.