Wisconsin native Jacob Kulke, 24, was stopped by Swift's security and later picked up by police when he allegedly attempted to hop the fence at her house on Friday (December 14).
Law enforcement sources disclosed to TMZ that Kulke claimed he was Swift's boyfriend and had come to celebrate her 23rd birthday on Thursday (December 13).
He also reportedly insisted that he had been in contact with Swift's handlers on social media before travelling to Nashville.
It is unknown if Swift was home at the time of Kulke's arrest, but there were reports earlier in the week that she was visiting the UK's Lake District with rumoured boyfriend Harry Styles.
Kulke - who has a criminal record - is currently being held on $10,000 (£6,205) bond.
Swift made news separately on Thursday when her song 'Safe & Sound' from The Hunger Games earned a Golden Globe nomination, which she described as the "best birthday surprise ever".