The music stars are said to have become inseparable over the last few weeks as they travel the world together on private jets after initially being linked last month when they were spotted on a series of dates at LA's Chateau Marmont.
And this weekend the 22-year-old 'RIP' singer was spotted getting cosy with the Scottish DJ and producer as he played a gig at the Grand Hotel in Las Vegas.
Calvin, 29, appeared to confirm the rumours after he posted a snap on Twitter of Rita boarding his private jet, which he captioned: "You again!"
A friend told The Sun: “They are having a great time and are really into each other.
“It’s early days, but they’re keen on each other.”
Last year Rita claimed she had turned down the chance to record the Calvin-penned Cheryl Cole hit ‘Call My Name'.
But an unimpressed Calvin took to Twitter to deny her claims, saying: “She made that up.”