The pair, who have recently spent many weeks apart, were briefly reunited before Christmas after Harry returned from his charity expedition to the South Pole, the Mirror reported.
But they have hardly seen each other since and, according to friends, they have been drifting apart, fuelling rumours that their relationship could soon be over.
It had been expected they would spend this last week together skiing in France but a source close to the Prince confirmed that the trip never took place, the report said.
"Talk of Harry and Cressida getting married could not be further from the truth. Indeed it wouldn't be a surprise if they go their separate ways soon," a source was quoted as saying by the daily.
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"It is actually Harry who has been moving on. He is incredibly fond of Cressida and loves her company but he has commitments and plans in other areas of his life that could be jeopardised by settling down. It is not what he wants at this time of his life," the source said.
It is understood that Harry and Cressida did get together the weekend before Christmas at Richard Branson's mansion in Kidlington, Oxfordshire, as guests of the tycoon's son Sam, 28, and his wife Isabella Calthorpe, 33 - Cressida's half-sister.
But they later went their separate ways - with Harry heading to Sandringham for Christmas.
It had been reported that Cressida, who recently graduated from dance school, was due to attend a dinner party at Sandringham hosted by Harry.
"Ironically it is Cressida who has thawed in recent months after initially being reluctant to make a long-term commitment," another source was quoted as saying.