A self-portrait by Rembrandt is expected to fetch around €15 million when it goes on sale in London on Tuesday evening.

The intricate work, measuring 17 by 22 centimetres, was painted in 1632 when the artist was in his prime and had just established his name with The Anatomy Lesson. Although around 80 Rembrandt self-portraits are known to exist, only three are in private hands, making the sale at Sotheby’s a rare opportunity for collectors.

It depicts Rembrandt in his finest garments – a black cloak, ornate lacework collar and felt hat – leading some experts to speculate that he may have painted it to impress the family of his fiancée, Saskia Uylenburgh.

Epco Runia, curator of the collection at the Rembrandthuis museum in Amsterdam, said: ‘It’s true that it’s one of the few self-portraits in which Rembrandt is wearing a smart outfit. Because the painting and its setting are so unusual, I think it was probably intended for private use. But maybe it was meant for his family in Leiden, so they could see how distinguished their son had become.’

Runia said he would prefer to see the painting come home to the museum, but it lacks the cash to buy a work that is estimated to fetch between €13 million and €18 million. ‘But never mind, we already have a lot of Rembrandts in the Netherlands. It’s not a disaster if people in other parts of the world can get to know him.’