A source said: "They have been seeing each other on the[down low]. It's only been weeks, so it's still pretty casual right now. They've been on a few dates."
Calvin - who split from Taylor Swift last month - met Tinashe in the studio in 2014 when they collaborated on the song Dollar Signs and were also rumoured to both be writing for Rihanna at the time.
Last week, Calvin hit out at Taylor - who is now dating Tom Hiddleston - after it was revealed she had written his song This Is What You Came For under a pseudonym.
In a series of tweets, he wrote: "Hurtful to me at this point that her and her team would go so far out of their way to try and make me look bad at this stage though.
"I figure if you're happy in your new relationship you should focus on that instead of trying to tear your ex bf down for something to do. I know you're off tour and you need someone new to try and bury like Katy etc. but I'm not that guy, sorry. I won't allow it.
"Please focus on the positive aspects of YOUR life because you've earned a great one "God bless everyone have a beautiful day (sic)".
Calvin also confirmed Taylor lent her vocals to part of his latest track and praised her lyrical abilities.
He tweeted after the report was confirmed: "And she sings on a little bit of it too. Amazing lyric writer and she smashed it as usual (sic)."
Calvin brought Rihanna in to record the vocals on the song as he and Taylor - who dated for 15 months - feared their relationship would overshadow the track if they released it together.
The so-called "breaking point" in their romance reportedly came after he was "disrespectful" by saying he'd never work with her while promoting the track.
