The so-called "Piano Man" has had an upright piano installed in his room at the secure mental health unit where he is being held, his carers have said.
The unidentified man was found in a soaking wet suit
Doctors are considering using music and art therapy to try to communicate with the mystery man who has not yet spoken.
More than 1,000 people from across the world have contacted a special helpline and several leads to his identity are being investigated.
The man, in his 20s or early 30s, was found in Sheerness, Kent, on 7 April.
The West Kent NHS Trust said on Friday that it may still be "some time" before it can establish who the man is.
A spokesman said: "We can now confirm that Mr X has a piano in his room and his clinical team are starting to explore both music and art therapies."
But he added that the man has yet to begin playing the instrument.
He added: "There has been no change in his condition.
"The Trust continues to work with the police to review and investigate the information that people have supplied."
The "Piano Man" is understood to be in good physical health but it is thought his psychological condition is unlikely to change dramatically in the near future.
The mystery man produced a pencil drawing of a piano
He has not said a word since being picked up by police after being found in a confused and dishevelled state.
Police have discounted claims he is a street musician from France.
When he was first found, staff at the Medway Maritime Hospital gave the man a pen and paper in the hope he would write his name, but he drew a grand piano.
His carers then put him in front of an instrument in the hospital chapel and he stunned them with a virtuoso performance. He has also composed music since being found.
The case has drawn comparisons with the Oscar-winning 1996 film Shine, which tells the story of acclaimed pianist David Helfgott who suffered a nervous breakdown while playing.