The 'Feel So Close' hitmaker is reportedly desperate to date the 25-year-old singer but she is playing hard to get.
A source shared: ''Yes, there is a spark there, but she's not an easy sell these days. She's giving it time and seeing what kind of guy he really is.
''She likes him, but she's not just going to jump into anything with him. She makes guys work for it because she wants to make sure that it's the right thing for her. At this point, he's still chasing her.''
The 31-year-old DJ - who previously dated Rita Ora - and the 'Blank Space' hitmaker sparked rumours they were an item when they were supposedly seen holding hands at last month's BRIT Awards.
And not only is Calvin interested in a romantic relationship with Taylor, he is believed to want to collaborate with her on some music.
Another insider added previously to HollywoodLife.com: ''Calvin doesn't just want to date Taylor. He's desperate to make sweet music with her. With his beats and her pop melodies, Calvin thinks they could produce a number of big hits together, and he's always been a big fan of Taylor's work.
''At the BRITs they discussed the possibility of exploring that, as well making sure they meet up in the US in between his regular DJ residency at Hakkasan in Las Vegas. It could be the start of a beautiful relationship professionally and personally, both are very talented artists and it would be a dream for their record labels if they teamed up.''
American Thighs was released on this day in 1994.