The 23-year-old singer has earlier dated former US president John F Kennedy's great nephew Conor Kennedy, reported the Sun Online.
"Taylor's desperate to get her name added on to the VIP lists of stars being lined up to meet Harry. She loves everything about him especially his ginger hair and English accent.
"She's dated John F Kennedy's great nephew Conor Kennedy, who is considered American royalty, and Harry would be a massive step up from him. Taylor is also Harry's type as he loves blondes," a source said.