Atletico visit Real at the Santiago Bernabeu today, having gone four matches without a defeat in the league at their opponents' backyard.
Barcelona have an 11-point lead over Atleti at LaLiga's summit with seven games of the season remaining.
Griezmann indicated last month that he would decide on a move before the World Cup finals in Russian Federation, which start on June 14.
The home side were aggrieved not to be awarded a penalty after Toni Kroos went down under Juanfran's clumsy challenge two minutes later, and the Germany global let his frustration show when he was booked for a needless foul on Griezmann.
Atletico actually had the ball in the back of the Real Madrid net in the 19th minute, but Diego Costa was adjudged to have felled Sergio Ramos in the build-up, before Oblak did well to keep out a Ronaldo strike down the other end.
Ronaldo tested Jon Oblak from distance in the 20th minute while Varane came close to open the scoring in the 28th minute.
Atletico Madrid striker Antoine Griezmann has rubbished reports claiming a move to Barcelona is already in place but says he wants his future sorted before the World Cup in Russian Federation later this year.
Ronaldo was surprisingly replaced by Karim Benzema in the 63rd minute of the match, while Atletico boss Diego Simeone also made alterations during the same period as Gabi and Angel Correa were introduced, with Costa among those leaving the field.
But it was skipper Sergio Ramos who nearly won it at the death when his free-kick looked to be heading into the top corner until Oblak got a hand to it.