Madrid have endured a hard campaign, sitting 19 points behind Barca in La Liga, and meet PSG in the Champions League last 16 on February 15.
Real were 4-0 up at the break at the Bernabeu after a blistering first-half display, which included a goal in the first minute from Vazquez.
"He's a superb player and he's shown that, it's not true we want to sell him", Zidane told a press conference on Friday ahead of Real Madrid's La Liga home match against Real Sociedad, reports Efe.
"I don't need to prepare anything", Zidane said. While Sociedad have scored 41 goals this season, the fourth most in La Liga, they leave themselves vulnerable defensive.
But sloppy defending allowed Jon Bautista and Asier Illarramendi to score late consolations for the visitors, although Cristiano Ronaldo completed the scoring by wrapping up a ideal hat-trick.
Madrid fans voted Wales forward Gareth Bale their player of the month for Janaury but the other member of their famous attacking trident, Karim Benzema, has fallen on hard times in terms of form and goals.
Los Blancos wasted no time in gaining the upper hand, breaking the deadlock in the opening minute of the game.
While Ronaldo leads the club with eight goals, he has lost half a step this season and has been unhappy with the club.
The goal was Neymar's 19th of the season in just 18 Ligue 1 matches and the Brazilian has provided 11 assists so far.
"I think we're ready for Real".
"We know that he always wants to score and generate chances", Zidane said of the 33-year-old.