The couple - who have been dating since October - are believed to have called time on their romance in December and spent the festive season apart.
An insider told People: "They`re over. It ended last month."
It has been claimed the 30-year-old actor - who was previously in a relationship with Reese Witherspoon - decided to end his romance with the 21-year-old country singer because he felt "uncomfortable" with the couple`s nine-year age gap.
A source told Us Weekly magazine: "Jake reached out to her and started all of this, but now he`s not acting as interested. He said he wasn`t feeling it anymore and was uncomfortable with all the attention they got.
"He also said he could feel the age difference. Taylor is really upset. We told her not to move so fast with this but she didn`t listen. Jake cares about her, but the publicity was a lot for him. He wants to keep his private life private, and that`s hard to do dating Taylor."
Only last month, the `Love and Other Drugs` star admitted he gets very frustrated by the interest in his personal life because he worries it will affect his relationships.
He said: "It bothers me a little that there is so much interest.
"One of the greatest parts about being in a relationship is the intimacy you share - but it can be difficult if you`re being watched the whole time. But I understand - it`s just one of those things."