The Royal Academy wants Damien Hirst to join the art establishment and follow other Young British Artists, including Tracey Emin, to become a member.

But it is understood that Hirst, the now enormously wealthy enfant terrible of the British art scene, has reservations about taking up the offer - and may be on the verge of turning it down.

His was one of the names discussed at last week's meeting of the RA assembly which runs the affairs of the institution dating back to 1768.

He is the logical next step in membership after last year's election of Emin who has curated one of the galleries at this year's Summer Exhibition and included a work by Hirst.

Other big names among London's contemporary artists such as Gary Hume and Fiona Rae are also already Royal Academicians - as is Michael Craig-Martin, who taught Hirst and Rae at Goldsmiths College.

Emin made clear her desire to join the ranks of David Hockney, Peter Blake and Antony Gormley. But Hirst, who will be 43 on Saturday, is arguably a more maverick figure. One source at the Royal Academy said they were very keen to have him but there were sensitivities involved. It is understood Hirst was not immediately convinced that he should accept an offer now.

In the past, some established artists have expressed doubts about Hirst's work. Speaking nearly a decade ago, John Hoyland, who had just been made professor of painting at the Royal Academy School, said: "As for Hirst, he is becoming an entrepreneur and I don't think that's a good thing. Artists should not farm their work out. I hear that he has lots of people working on his spin paintings. I don't see how you can have a humanity in your work if you do that."

In return, Hirst was sniffy about the RA. At the time of the ground-breaking Sensation show of Young British Artists from the collection of Charles Saatchi held at the Royal Academy in 1997, he called it "a big, fat, stuffy old pompous institution". But 2008 is the 20th anniversary of Freeze, the show regarded as having seminal status in the story of the YBAs.

Curated by Hirst and students from Goldsmiths, it introduced many of them to the wider art world. Hirst has since become a millionaire thanks to his spot paintings and cows and sheep in formaldehyde. The Physical Impossibility of Death in the Mind of the Living, a 14-foot shark in a vitrine, is regarded as one of the most important pieces of art of the last 50 years. Last year he produced a £50 million diamond skull. Saatchi has named Hirst, who won the Turner Prize in 1995, as the one contemporary artist who will be known to future generations.

Although being made a Royal Academician is regarded as a prestigious accolade, not all of Britain's best artists have been elected or accepted the offer. Lucian Freud, for example, is not an RA.

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