The Wellcome Collection features art and medical artefacts
The Wellcome Collection has said if it wins this year's Arts Fund Prize, it will give the £100,000 prize money away to the losing finalists.
Clare Matterson of the Wellcome Trust told Radio 4's Front Row the London- based museum did not need the cash.
"But we would be honoured and thrilled to receive the prize as a recognition," she said.
The winner will be announced on 22 May at the Royal Institute of British Architects in London.
The Lightbox in Surrey, Shetland Museum and Archives in Shetland and the British Empire and Commonwealth Museum in Bristol are also competing for the prize.
The Wellcome Collection, which opened in 2007, displays a mixture of medical artefacts and artworks exploring the connection between medicine, life and art.
"If we won that £100,000 we would want to give it to others, we would not want to keep the money," Ms Matterson said.
"I've looked at all the others on the list, I've visited a couple of them. So for us, if the others would like to share the money between them, that would be a wonderful outcome for all of us."
Rosemary Ewles, administrator of the Art Fund Prize for museums and galleries, said: "This is very generous if not a little unusual. It'll be interesting to see what happens but it's important to note that any plan proposed by a museum or gallery should they win, has no bearing on the judges' decision."
Last year's winner was Pallant House Gallery in Chichester.
The Art Fund Prize for museums and galleries is awarded for originality, imagination and excellence.
It is also intended to increase public appreciation and enjoyment the museums and galleries have to offer.
You can hear the full report on Front Row on Thursday at 1915BST on Radio 4.