The allegation has been made by the singer’s girlfriend of the time, Cecilie Thomsen.
Thomsen says Adams and the Princess began the affair after she separated from Prince Charles.
Her claim comes after former Royal butler Paul Burrell said Diana had nine suitors – including a leading musician.
Adams, however, said Cecilie knew nothing of his relationship with Diana and added that reports of an affair were conjecture. But The Sun says he has refused to deny the claims outright.
Thomsen, who appeared in the James Bond movie, Tomorrow Never Dies, said: “Bryan knew Paul Burrell very well and Paul was part of the inner circle around Bryan and he also introduced him to Diana.
“The first time Bryan met Diana I wasn’t invited. Ours was a stormy relationship and Bryan’s affair with Diana didn’t make it easier.” Cecilie attended Diana’s funeral with Adams.
In 1985, four years after Diana married Prince Charles, Adams wrote a song called Diana. One verse says: “Oh, the first time I saw you was in a magazine, The next time you was walking ‘cross my television screen, I knew right then and there that I had to make you mine, That day he married you I nearly lost my mind.”
Speaking about Diana earlier this year, Adams said: “We met many times and had become very good friends by the end of her life.”
Ananova.com