The singer and TV presenter, who found fame at the age of 12 with his top five Christmas hit Walking In The Air, said he was "deeply sorry" for any upset caused but strongly denied any "inappropriate contact".
A spokesman for the 46-year-old said that while the matter does not relate to any broadcast work, he had voluntarily agreed not to go on the BBC while it is investigated.
In a statement, the spokesman added: "Whilst he accepts that his behaviour over a decade ago was occasionally juvenile, as was that of others, he never intended to harass or distress and he strongly denies any inappropriate contact.
"He is, however, deeply sorry for any upset caused and hopes this matter is resolved soon."
The former choirboy received an MBE in 2013 for his services to music and broadcasting.
He became a national radio presenter after signing up with Classic FM in 2002 and went on to present a Sunday morning show for BBC Radio 2.
Jones, a father of two, was a contestant on Strictly Come Dancing in 2004 and further TV work has included Daybreak, Escape To The Country and Cash In The Attic.
The BBC has declined to comment.