It was sold by celebrity jeweller Harry Winston some 60 years ago and has been in a private collection ever since.
It is now on show in Hong Kong and will tour the world before being sold by Sotheby's auction house in Geneva.
It is estimated to fetch between £17 million and £24 million – almost one million pounds per carat.
The current world record for the most expensive diamond sold at auction per carat is the Star of Josephine, a blue diamond weighing 7.03 carats which sold in May 2009 at Sotheby's for six million pounds – £850,000 per carat.
David Bennett, of Sotheby's, said: "During my 35-year career I have had the opportunity to examine many magnificent and rare gemstones.
"But, put simply, this stone is one of the most desirable diamonds I have ever seen.
"What makes it so immensely rare is the combination of its exceptional colour and purity with the classic emerald-cut – a style of cutting normally associated with white diamonds and one that is so highly sought-after when found in rare colours such as pink and blue.
"The stone's character is further enhanced by the gently rounded corners which impart a unique softness and charm to this truly outstanding gemstone."
The coloured diamonds are described by experts as the most sought-after jewels around the world, with blues, pinks and greens proving most popular.
Once sold, the stone is expected to rocket into the list of the top ten most expensive diamonds in the world.
This list ranges from the Allnatt Diamond at number ten, worth a comparatively paltry £1.9 million, to the priceless Koh-I-Noor, one of the British crown jewels.
The famous Hope Diamond is currently classed at number four in the list, with a £220 million price tag,
Fellow pink diamond, the Steinmetz Pink, is currently at number six, valued at £16 million.