The dispute over who owns the artefacts has been on-going for past two centuries.
The marbles, which in the early 19th century were removed from the Athens Parthenon and taken to the British Museum, will not leave London, spokeswoman for the British Museum Hannah Bolton told AFP.
Greek Culture Minister Evangelos Venizelos had proposed a shared exhibition of the marbles between the British and the New Acropolis museums for the 2004 Olympics.
Bolton told AFP she was discussing a possible virtual show to exhibit the Elgin Marbles with a number of museums.
Since its independence in 1832, Greece had repeatedly requested the return of the 2,500 year old antiquities.
The fifth-century BC marbles include 56 sculpted marble plaques originally forming the eastern frieze of the Parthenon, together with 12 statues. British ambassador Lord Elgin first removed the antiquities with the permission of Greece's then Ottoman rulers.
In Athens, work has started on a $74 million Acropolis Museum, designed specifically to exhibit the marbles.