A small self-portrait by Rembrandt expected to fetch €15m at auction at Sotheby’s in London on Tuesday has changed hands for €16m, the top end of the estimate.

Six bidders vied for the portrait, one of three of the Dutch master still in private hands.

The intricate work, measuring just 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. 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.

The name of the buyer has not been made public but Rembrandt expert Jan Six told talkshow OP1 on Tuesday that according to his sources he or she is thought to be ‘a trophy buyer, not someone who is used to buying old masters’.

Epco Runia, curator of the collection at the Rembrandthuis museum in Amsterdam said he would have preferred to see the painting come home to the museum, but that it lacked the cash to buy the work. ‘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.’

The last time a portrait of Rembrandt was auctioned was in 2003. The artists is known to have made hundreds of self portraits, including sketches and etchings.