A junior membership card with the name of Prince George Alexander Louis, the first child of Prince William and his wife Catherine, was handed to British ambassador Nigel Casey at the club's Sarajevo stadium.
"England is a cradle of football... The love of football links the United Kingdom and our country," said a club statement.
"It should not be forgotten that he is also a grandson of the tragically killed Princess Diana who has been remembered in our country for her humanitarian work and help in mine clearing" after the 1992-1995 inter-ethnic war that left some 100,000 dead.