Is Roy based on Quentin Tarantino and Sofia Coppola?

Yes. According to The Times of India it's based on/inspired by their affair.

Initially, they cited a source close to production who commented:

Vikram (Vikram Singh, the director) is a fan of both the filmmakers and he wanted to create a narrative around the affair between the two movie greats.

They later confirmed this directly with Vikram Singh:

When contacted, Vikram Singh confirmed the news, saying, "The Tarantino-Copolla affair has definitely inspired our plot. And I've had several discussions with my cast about the same. Both Jacky and Arjun have been reading up extensively about the two directors to get the nuances of their personalities right," he said.

Edit:

I suppose it depends on whether you consider inspired by to be as good as based on. The fact the director has confirmed the two leads have been reading up on the two directors' personalities is enough for me to stand by my claim. Even if they haven't followed Tarantino/Coppola to the letter, it certainly seems it was based on their doings (with some artistic license as well).

No. First of all we have to see where does this claim come from. You would have probably read this in a TOI article (Sorry unable to post the link).

If you revisit that article, it seems more like a inspired by thing rather than being a based on thing.

The director of Roy claims to be a fan of Tarantino and Copolla and yes the two directors did have a two year affair, but let's try to examine what are the parallels between the movie's story and actual story.

1. Tarantino has not been called or seen as a casanova, unlike the movie's character.
2. Tarantino and Copolla are not two filmmakers based in different countries, unlike the movie's plotline.
3. Tarantino and Copolla have not reunited after a split. Well at least not until now :-)

So as you can see, apart from the fact that the story is about a love affair between two movie directors, there is nothing else.

But a mere linking of the story with some real life celebrities does spark an interest among the viewers, which is good for the business ;-)

So that's my take on this topic.

EDIT : While Andrew Martin's answer is factual, I would like to discuss a few things. The sources cited by Andrew Martin are correct, but aren't they the same sources which intrigued the OP into asking this question ? Yes, the director claims that the story is based on real life characters, actors read extensively about the personalities and tries to get the nuances right. But this is what the claim is. OP wants to know whether this claim is right or not and we can answer this after analyzing the movie's story and trying to draw parallels between movie's characters, plot lines and the actual stuff. And as I stated earlier, there are none other than the fact the movie's characters are two directors. Tarantino and Copolla are not the only two directors who dated each other. It would be interesting to know what similarities are there.

To me this claim is as good as Fargo's (TV series) - "Based on True story".