The singer-songwriter has befriended the country star after he collaborated with her on her latest album Red.
Sheeran will also join Swift on 45 dates of her upcoming North American tour in 2013.
The pair are said to have been regularly messaging each other, and are getting "increasingly close", according to The Mirror.
He has now reportedly got a tattoo of the word 'Red' - the name of Swift's new LP - on his arm.
The body art was completed by One Direction's tattoo artist Kevin Paul at Birmingham's Radisson Blu Hotel.
Swift recently revealed that she spent hours singing and laughing with Ed Sheeran while writing songs for her album.
The US country singer has collaborated with the British star on the track 'Everything Has Changed'.
Listen to the duet below: