Madrid have now failed to beat Atletico in their last five league games at the Bernabeu (two draws, three defeats).
Griezmann indicated last month that he would decide on a move before the World Cup finals in Russian Federation, which start on June 14.
Juanfran was fortunate to see a challenge go unpunished when Kroos darted into the box on the end of a short corner and frustration seemingly lingered for the Germany midfielder as he was booked for a crude hack at Griezmann on halfway.
And the Atletico goalkeeper yet again thwarted the Champions League holders in the 27th minute, as he reacted quickly to deny Raphael Varane from firing in from close range.
But it was Zidane's men who came desperately close to taking the lead with three minutes of the half remaining when full-back Marcelo cut inside and unleashed a right-footed shot which cannoned back off the bar with Oblak producing a fine save to keep out Dani Carvajal's equally fierce follow-up.
'Nanny state full of PC snowflakes' - Sugar tax sparks anger
The money raised from the tax , which will affect drinks such as classic Coca Cola and Fanta, will then go to the Treasury. A tax on sugary soft drinks has come into force, meaning consumers will have to pay more for their favourite refreshments.
Ahead of Sunday's Madrid derby (16:15, CEST), Antoine Griezmann is arguably playing his best football since joining Atlético, and his 24 goals this campaign and general play has turned heads even further around Europe.
Atletico's clearest chance of the first period arrived on the half-hour mark when Costa broke into the Real Madrid box, but the Brazilian-born Spain global saw his low strike saved by Los Blancos stopper Keylor Navas.
On Griezmann, Atletico coach Diego Simeone said: "He is a great player, he did not have a good start to the season and he knows it and it is not easy to reinvent himself in the way he did in November, December".
Navas then made a smart stop from Koke as Atletico tried to maintain momentum, while another counter-attack saw Saul slide an effort just wide from 20 yards.
Atletico had a huge chance to score a second in the 82nd minute when Griezmann delivered a low cross towards Correa, but the Argentine, who was unmarked, just could not make contact.
Ronaldo continued a phenomenal 2018 when he volleyed Madrid into a deserved 53rd-minute lead at the Santiago Bernabeu - his 40th goal in all competitions this season.