The couple will therefore break with tradition by not being buried together in the Roskilde Cathedral when the time comes.
Henrik was born in France in 1934, and married 77-year-old Queen Margrethe back in 1967.
They met in London, where he was stationed as a diplomat, when she was the crown princess.
The 83-year-old was named her Prince Consort when she became Queen, but he has repeatedly said he would have preferred to have been named King Consort instead.
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In Denmark, princesses have traditionally been named Queen when their husbands take the throne.
Lene Balleby, a spokeswoman for the Royal Danish House, told the BT newspaper: “It is no secret that the Prince for many years has been unhappy with his role and the title he has been awarded in the Danish monarchy.
“This discontent has grown more and more in recent years.
“For the Prince, the decision not to be buried beside the Queen is the natural consequence of not having been treated equally to his spouse – by not having the title and role he has desired.”
The spokeswoman confirmed that Prince Henrik’s decision had been accepted by the Queen.
When Queen Margrethe dies, she will be interred in the Roskilde Cathedral in a sarcophagus made by Danish artist Bjorn Norgaard.
It is not clear exactly where Prince Henrik will choose to be buried, but Ms Balleby said it would definitely be in Denmark.
Prince Henrik has carried out very few official duties since he retired last year and renounced his title of Prince Consort.
Since then, he has spent much of his time at his private vineyard in France, despite still being married to the Queen and still officially living together.
The couple has two sons, Crown Prince Frederik and Prince Joachim.
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