The watercolour by Liverpool marine artist Arthur Knowles, which shows the stricken Titanic hitting the iceberg on its maiden voyage on April 15, 1912, will be sold at fine art auction house Halls on March 18.
It carries an estimate of up to £500.
Allan Darwell, head of Halls' art department said that the watercolour was commissioned by a cousin of Wallace Henry Hartley, bandleader and violinist aboard the Titanic.
Mr Hartley became famous for leading the eight-member band as the ship sank and they all perished.
Survivors reported that Mr Hartley, 33, and his fellow band members started playing music to help keep passengers calm as the crew loaded the lifeboats.
Many said that he and the band continued to play until the very end.
Mr Hartley's body was recovered almost two weeks later and, according to press reports, was "fully dressed with his music case strapped to his body".
The funeral took place in his home town of Colne on May 18, 1912 and was attended by 1,000 mourners, while an estimated 40,000 lined the route of his procession.
"As there is always an enormous amount of international interest shown in Titanic memorabilia, we have decided to include the watercolour in our fine art sale on March 18," said Mr Darwell.
"This memorabilia is so sought after because of its rarity and the provenance of this painting could add to its value.
"Arthur Knowles is more renowned for his oil paintings, several of which are held in the Maritime Museum in Liverpool."