Cardinal Keith O'Brien was reported to the Vatican by three serving priests and a former priest, according to The Observer newspaper.
He contests the allegations, said to stretch back to the 1980s, and is taking legal advice.
Cardinal O'Brien is the head of the Catholic Church in Scotland. He has been the Archbishop of St Andrews and Edinburgh since 1985.
The 74-year-old, who is due to retire next month, originally comes from Ballycastle in Co Antrim.
The claims emerged just days after Cardinal O'Brien called for the Catholic Church to end its celibacy rule for the priesthood.
The cardinal is also an outspoken opponent of plans to legalise same-sex marriage.
He is the only British cleric able to vote in the upcoming conclave to elect a successor to Pope Benedict XVI following his decision to resign.
He previously said he has not yet decided who should be elected as Pope during the conclave, which is expected to be held next month.
It was reported that Cardinal O'Brien missed Sunday Mass at St Mary's Cathedral in Edinburgh.
No spokesperson was immediately available to comment.