European publications have been speculating on the pair's relationship since an article appeared in Spanish newspaper ABC on Saturday, suggesting the princess did not attend the recent coronation of new Dutch King Willem-Alexander with husband Prince Albert II because she was in her native South Africa with Kelleher.
Kelleher is known to be a close friend of the royal couple, attending their 2011 wedding and holidaying with them on Italy's Amalfi Coast last year.
''Rumours about a relationship between the two have erupted,'' the newspaper said.
Since then, French, German and Italian newspapers have published the story, with headlines such as ''Charlene of Monaco and rugbyman Byron: An affair in the works?''.
ABC said Kelleher was an ''intimate friend'' of Charlene and accompanied the 35-year-old princess to a recent tennis tournament in Monte Carlo.
Kelleher's father, kiwifruit orchardist Kurt Kelleher, dismissed the reports when contacted in Te Puke by the Otago Daily Times last night. ''They have been friends for some time, but it is untrue that he was in South Africa with her,'' Mr Kelleher said.
''He has been working for her sports foundation in Monaco for a number of months. It is mere speculation and the royal palace has also not commented on it.''
Kelleher was in a relationship with porn star Kaylani Lei in 2005.
The 36-year-old attended Otago Boys' High School and played for Otago in the NPC and the Highlanders in the Super 14, before moving north in 2004 to play for Waikato and the Chiefs.
He played 57 tests for the All Blacks between 1999 and 2007. Following the 2007 World Cup, Kelleher played for French club Toulouse and in 2011 joined the Stade Francais Club in Paris. He left last April, a year before his contract was due to expire.
Since then, he has been in charge of rugby projects for Princess Charlene's sports charitable trust, the Princess Charlene of Monaco Foundation. Kelleher's former Highlanders and All Blacks team-mate Josh Kronfeld told the New Zealand Herald the reports ''wouldn't surprise'' him.
''If anyone can meet women, it's him,'' Kronfeld said.
