The duo have known each other for two years now.
Harris, 32, met Tinashe, 23, 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, reported the New York Post.
"They have been seeing each other. It's only been weeks, so it's still pretty casual right now. They've been on a few dates," a source said.
The couple were seen on a date at Nobu in Malibu on July 16 and their affection for one another was clear to see.
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