In a series of allegations to be published in a new autobiography by Tasha de Vasconcelos, the 42-year-old claimed the Prince "flirted" with her under the nose of Camilla Parker Bowles at the party in 1999, the 'Daily Mail' reported.
A Clarence House spokesman, however, said: "We never comment on private conversations."
In fact, the Mozambique-born model claimed in her book 'Beauty As A Weapon' that they began with a "clumsy" chat -up line and "seductive smile" from Prince of Wales, but soon accelerated during the 1999 party.
"During the evening, I saw his eyes glance over my necklace, which lit up my face, and to the more intimate attractions of the curves beneath my Versace dress.
"The Prince had become a man. 'You are magnificent', he dared to utter. 'Would you ever consider a private catwalk show... just for me?'" she was quoted as writing in her book.
The model said that she turned down the request as she was "disconcerted by all the other diamond-encrusted women listening in around us" and "had read that the great love of his life was called Camilla".
She claimed that she met Charles, now 62, for the first time at a polo match in Cheltenham that year after being introduced by Aurelia Stephenson, a publicist who was the then girlfriend of Prince Andrew.
Subsequently, Vasconcelos and Charles met several times and she was invited to Clarence House and to a private lunch with the Prince at an unidentified palace, she said.
The model -- who now lives in Monaco and counts France's First Lady Carla Bruni Sarkozy among her close friends -- has denied persistent rumours about a relationship with Prince Albert of Monaco.