The 29-year-old has made 215 appearances for Madrid in all competitions but his contract with Los Blancos will expire next June, and there has recently been speculation surrounding his future.
Vazquez has been a regular at club level during the 2020-21 campaign, making nine appearances in all competitions, including the full 90 minutes against Inter Milan in the Champions League on Wednesday.
After the 2-0 victory at San Siro, Zidane lavished praise on the Spaniard and hinted that the versatile attacker could soon pen a fresh contract in the Spanish capital.
"He always gives everything for us. I have always valued him and what he gives to us on the pitch," Zidane told Movistar+.
"Now he is having the opportunity to show us what he is all about. He was a youth player for us and has Madrid in his heart.
"I'm happy for him and the team. He is an important player and the club knows it. I think it will happen that he will renew."