Zidane made the announcement after injury-plagued Bale returned to training on Friday morning, but despite being available for the Club World Cup, which started on Wednesday with host club Al Jazira's 1-0 win over New Zealanders Auckland City, both the Wales winger and Varane will miss Saturday's visit of Sevilla in La Liga.
Bale has yet another calf injury and Varane is suffering from a muscle problem.
"Bale won't be available tomorrow (Saturday) but the idea is that he will travel with us to the Club World Cup and will see if he can play in the first match," said Zidane.
Real will begin their tournament campaign as strong favourites against one of Al Jazira and Japan's Uwara Reds in their semi-final on December 13th.
Centre-back Varane limped off in the 38th minute of Real's 3-2 Champions League win over Borussia Dortmund on Wednesday, and his time on the sidelines comes as Zidane has to deal with a defensive crisis ahead of Sevilla.
Sergio Ramos, Dani Carvajal and defensive midfielder Casemiro are all suspended and youngster Cesar Vallejo is also injured.
However Zidane is confident that 24-year-old Varane will recover in time to play in the UAE.
"Rapha's injury is not serious. He won't be with us tomorrow but he underwent an MRI scan and nothing big came up," he said.
"He will come with us to the tournament and we'll see if he can play in the next match."