The couple - who went public with their romance in June - are reportedly on the rocks over how "public" Tom wants the relationship to be.
A source told DailyMail.com: "Tom wants their relationship to be public, even asking Taylor to go to the Emmys with him, but Taylor wants to keep her private life private.
"Tom's need for their relationship to be so public so quickly makes her uncomfortable.
"She tried to be OK with it in the beginning but fears he is in love with the idea of her and not falling in love with her for the right reasons.
"Taylor is an independent young woman and doesn't feel like she needs a boyfriend to make her complete."
While Tom, 35 and 26-year-old Taylor were inseparable at the beginning of their romance, they have been apart recently while he films 'Thor: Ragnarok' in Australia.
They met at the Met Gala in May, while Taylor was still dating Calvin Harris, and struck up a romance a few weeks later after she split from the 32-year-old DJ.
Meanwhile, Tom was previously forced to deny claims their relationship was a "publicity stunt".
He said: "Well, um. How best to put this? That notion is - look, the truth is that Taylor Swift and I are together and we're very happy. Thanks for asking. That's the truth. It's not a publicity stunt."
And he insisted he didn't care what people thought of his relationship because he was being "authentic" and true to himself.
When asked if the focus on his personal life annoys him, he said: "I don't know, it comes down to being authentic.
"Everything you do you have to make sure you truly believe in it and as long as you know that, it doesn't matter what anyone else says about it because the nature of being a public figure is that everyone will have an opinion about anything you do, and as long as you know why you've done something and you've committed to it with authenticity then you're OK."