Paul Chandler, from Tunbridge Wells, Kent, and his wife Rachel have been held for more than four months after they were captured while sailing from the Seychelles towards Tanzania.
A photographer who has filmed the couple since they were captured said the pirates have requested medicine to treat Mr Chandler's eyes. Mohamed Dahir, a Somali freelance photographer, said the group contacted Dr Mohamed Helmi Hangul, in Mogadishu.
Mr Chandler is reported to be suffering from trachoma, which is caused by the chlamydia trachomatis micro-organism and is spread by flies or through contact with an infected person.
The British Government has refused to pay a ransom for the couple and called for their immediate release.