According to Spanish newspaper Marca, the proposed offer is already on Zidane's desk in Valdebebas, and only needs a signature to confirm the deal.
Sevilla are the visitors to the Bernabeu on Sunday, with Real needing seven points from their last three games to secure a first LaLiga success since 2012.
The two football giants Real Madrid and Juventus are due to battle it out in Cardiff in the upcoming Champions League final.
This year also the tournament was well fought by the teams but now only two teams have left, Real Madrid and Juventus.
Real's Champions League triumphs in 2014 and previous year have distracted from rivals Barcelona's creeping domination in the domestic league, with the Catalan side winning five of the last seven titles.
Barca know, with only head-to-head record keeping them above Real Madrid, who have a game in hand, victory is imperative if they are to defend their title.
"And yes, he was a great player and could turn out to be a great coach".
Real Madrid have failed to explain the reasons behind his absence from the workout but even if it's only a precautionary measure Zidane may consider to give him a rest against Sevilla. Madrid goalkeeper Keylor Navas got his glove to the ball, but couldn't keep it out.
Atletico Madrid forward Antoine Griezmann remains his preference, while the likes of Andrea Belotti and Neymar are also touted as targets, but based on the money involved and if there is an openness to negotiate, then perhaps Bale could become a more serious candidate in the coming weeks. They have beaten some quality team on their way to final.
The 11-times European champions, who were playing in their seventh consecutive semifinal and targetting a 15th final berth, waited for Atletico to run out of steam and Isco delivered a knockout blow before halftime to make it 2-1, putting them 4-2 up on aggregate.
Before the half-time break, Diego Godin, Gabi and Sergio Ramos had joined them in the referee's book, all for protesting as the referee let several tough challenges go unpunished.
The hosts have already locked up their ticket for next year's UEFA Champions League, but Liverpool, Arsenal and Manchester City are still hoping to beat Manchester United in the race.