The 'Blank Space' singer was seen flirting with the Scottish DJ - who recently split from girlfriend Aarika Wolf - at last month's BRIT Awards and they have reportedly been in regular contact since then and were inseparable when the 25-year-old star visited Las Vegas, where Calvin has a residency, last week.
A source said: ''Taylor and Calvin are into each other in a big way. It's early days but there's an undeniable connection between them and they've been texting pretty much every day.
''They had a lot of fun in Las Vegas and she especially enjoyed hanging out after the show.
''Taylor has told friends she can't get him out of her head. Everyone thinks this could have serious potential.''
It is believed Taylor - who previously dated Harry Styles, and Conor Kennedy and was linked to singers Tom Odell and Matt Healy - and Calvin were introduced by mutual friends Ellie Goulding and Haim and all of Taylor's pals are hoping the romance works out.
The source added to Grazia magazine: ''They have so much in common. Her friends totally approve, which is a plus
''What's more, everyone knows she has a soft spot for British men. The fact Calvin is so well-mannered and creative is a bonus too.''
They might sound like they're from the 70s, but they way they roll is very 2020.
What's new in the music world this week?
'U Kin B the Sun' is an album rich in texture and depth and one that quite obviously, and unapologetically, plays to Frazey Ford's strengths.
Listen to their new single 'Small Change'.
Everything you ever needed to know about Viking metal.
3TEETH hit Leeds for the first time with support from British artist PIG.
This will make you want to walk amongst the skyscrapers.
Yet another teen sci-fi adventure, this movie may be sharply well-made but it struggles to...
Author Lois Lowry talks about her dystopian sci-fi book 'The Giver' in a featurette ahead...
Dr Seuss' eco-fable is transformed into a raucous adventure comedy in this colourful animated feature....
Watch the trailer for Valentine's Day *Chick Flick Alert* Valentine's Day is a romcom set,...
Watch the trailer for Hannah Montana The MovieHannah Montana has had the feature film treatment....