The couple were brought together by Taylor Swift, sources told the magazine. Swift, who is now touring with Sheeran and is a Gomez pal, reportedly introduced them Memorial Day weekend.
"They are hooking up," one source described as an insider said.
Gomez, 20, has been in the public eye since she appeared on "Barney and Friends" with a certain purple dinosaur at the age of 10. She went on to appear in a number of Disney Channel programs and to an off-again on-again relationship with Justin Bieber that now appears to be definitely off.
Another source told Us that Gomez finds Sheeran, 22, more mature than her 19-year-old ex: "She got sick of having to take care of Justin like he was her child. This is a nice escape from the drama."
Another party suggested that Sheeran and Gomez are not yet a serious item.
"They are friends with an open mind," the person said. "He's sensitive and sweet and a lot deeper than Justin."