Press Association cited an unidentified source as saying that Harry, 29, and Bonas, 25, had decided to end their two-year relationship. Other news media — including the BBC, the Daily Mail and The Sun — also reported the breakup, giving no sources.
Royal officials declined to comment.
This year, Harry shifted his military career from flying Apache helicopters to organizing army events as a staff officer, meaning he could see Bonas more often. Speculation about a possible engagement had been rife since Bonas and Harry appeared together at an official charity event in March.
Harry is the grandson of Queen Elizabeth II and is fourth in line for the throne.