The duo - who share a manager, Scooter Braun - recently collaborated on the song 'Almost Is Never Enough' for 'The Mortal Instruments: City of Bones' soundtrack which reportedly led to a romance.
A source told Us Weekly: ''It's very, very new. Nate sends her flowers everyday.''
Ariana, 20, recently gushed about Nathan in an interview, praising his work on their duet.
She said: ''Nathan just sang the hell out of it. I thought it was Brian McKnight. I'm like, 'Who is this?' Honestly, I wasn't expecting it. I didn't know he had that in him. I saw him perform live on one of the radio shows that we were at together, and I was like, 'Damn, he can sing.' This song I think will pleasantly surprise a lot of people. It's very beautiful and very emotional and I love, love, love what Nathan did to it. It was a great, great, great surprise.''
The 'Sam & Cat' actress previously dated YouTube star Jai Brooks of the Janoskians and was recently linked to Justin Bieber.
Corgan took to Instagram to confirm rumours of new Pumpkins material, saying the first songs could arrive as early as May.