According to Heat, the X Factor USA boss wants his fellow judge to get on with the singer to give both his show and the group publicity.
"Demi is being spurred on by Simon, who finds the whole thing very amusing," an alleged insider told the magazine.
"He's also adoring the publicity it's giving both his band and The X Factor - it's a win-win."
The supposed friend of Lovato claimed that the pair are texting each other every day and that the One Direction man is "totally besotted" with her.
"He's very keen," they continued. "He's been sending her flowers.
"She thinks he's really cute. She can't wait to get to know him properly when he's finished the One Direction tour at the beginning of July."
Horan confirmed last week that he had been in contact with Lovato, calling her "really nice" but adding: "I don't know what's going to happen."