The marbles are housed in the British Museum
Swiss-American architect Bernard Tschumi won the commission for the £29m museum with a design topped with a glass structure to show off the sculptures to their best advantage.
The ancient sculptures, now in the British Museum, were removed from Greece more than 200 years ago by British ambassador to the Ottoman Empire Lord Elgin.
The Greek Government has long fought to have the artefacts returned to their homeland and is still confident it will get its wish despite Britain's consistent refusal to hand them over.
The Greek Government announced in June its plans to build the Acropolis Museum at the foot of the Acropolis in Athens.
It made it clear then that the museum's primary function would be to house the marbles, although many other artefacts would also go on show.
'Commitment'
But, after weeks of deliberation over tendered designs, the Greeks are even more confident that Mr Tschumi's winning submission will seal their case for the return of the sculptures.
Dr Nicos Papadakis, a spokesman for the Greek Embassy in London, said his country was "forging ahead" with its claim over the marbles.
"This is the clearest manifestation of our commitment to have them returned. This shows that we mean what we say," stated Dr Papadakis.
The frieze originally came from the Parthenon, a temple on the Acropolis. Dr Papadakis added that, visually, the winning design for the museum would "reunite the sculptures with their natural site".
One of the main arguments against the return of the marbles was the lack of a safe place to house them in Greece.
When plans for the Acropolis Museum were confirmed, Greece's Culture Minister Evangelos Venizelos wrote to the UK Minister for Culture, Media and Sport, Tessa Jowell, asking for their return.
A spokesman for the DCMS said that the UK's position over the marbles "had not changed" despite the plans for the museum.
"Our view has not changed in that returning the sculptures to Greece would be unfeasible and, under its statute, the British Museum is not allowed to dispose of any of its pieces," he said.
Dr Papadakis said the Athens museum's first stone will be laid in the spring, with a view to it being completed in time for the Athens Olympics in 2004.
Dr Papadakis said although the museum would open, the glass gallery would remain empty until the sculptures were returned.