The 22-year-old singer has previously dated stars like Taylor Lautner, Jake Gyllenhaal and Joe Jonas.
"There were no public displays of affection between Taylor and Tim, but she surely looked happy to be there," Contactmusic quoted a source as telling US weekly.
"Yes, she has a crush on him. She is a massive fan, but I don't think he sees her that way," another insider added.
However, the 'Mean' hit maker is said to have embarked on a "friendship" with the 24-year-old hunk, rather than a romance.
"They actually have been speaking a lot about the Bible and Christianity. Right now it's on the friendship tip - even though that frustrates her," the source added.
The blonde beauty recently confessed she loves writing about her relationships and the ways they change, as she grows older.
She thinks that love is always a huge theme in what she writes about just because there are no two similar relationships, there are no two times that we feel love the same way or hurt the same way or feel rejection in the same way. It's always different and that fascinates her.