Harry, 29, recently confided in friends that things were not going well with the 24-year-old, The People magazine reported.
"He found her too needy and it just wasn't working out," a source close to the prince was quoted as saying by the magazine.
The couple were introduced by Princess Eugenie, a close friend of Bonas, who recently completed a postgraduate programme in dance studies at London's Trinity Laban Conservatoire of Music and Dance.
Harry yesterday met with wounded service personnel hoping to take part in the Invictus Games. Meanwhile, Cressida was spotted picking a healthy takeout from a juice bar.
A report in the Telegraph also said the couple had split.
The daily quoted sources as saying that they had "paused for a breather", suggesting that they could eventually get back together like the Duke and Duchess of Cambridge, who also split for a period.
"The relationship has certainly at least paused for a breather. It is virtually impossible to have a successful romance and relationship in the full glare of the world's media," a source was quoted as saying by the daily.
Last month the couple fuelled rumours that they might be about to announce an engagement when Bonas accompanied the prince to an official engagement for the first time.
The couple kissed and hugged at an event in Wembley Arena attended by 12,000 people, which was interpreted as a sign that they had grown more confident in the strength of their relationship.
Two days later the couple were again out together in public when they attended a Six Nations rugby match at Twickenham.
Bonas was known to have struggled to cope with the pressure of being talked about as a princess-in-waiting, but her public appearances suggested she had got over her nerves.