Danish magazine Billed Bladet has revealed that Mary, 37, and Crown Prince Frederik, 40, have made a number of secret visits to their obstetrician in recent weeks, arriving via a secret underground tunnel.

The magazine reports Mary and Frederik arrived at the Riget hospital - where Christian and Isabella were born - at around 6am and headed straight to the offices of Dr Morten Hedegaard, the princess's obstetrician reported the Australian Women's Weekly magazine.

Despite attempts to keep their visit under wraps, the couple were spotted leaving the hospital smiling and hand-in-hand.

The good news helped to cheer up devoted dad and sportsman Fred, who is facing six weeks in plaster after fracturing his leg while sleigh riding.

The palace has so far refused to comment on the talk.

"We do not speak about royal pregnancies before it is official," royal court communications manager Lene Balleby told Billed Bladet.

It is expected that Mary will wait until she is further along in the pregnancy before the couple make an official announcement.

Mary was well into her second trimester with Christian in 2005, and 14 weeks pregnant with Isabella in 2006, before confirming the good news.