The British Museum has again played down hopes of a loan
UK and Greek officials have held fresh talks on the Parthenon marbles, taken from Athens by Lord Elgin in 1806.
Greek demands for the sculptures' return will be discussed at a meeting organised by the UN in Paris in June.
Remarks by the director of the British Museum - saying items from the museum may be lent out - have heartened supporters of the marbles' return.
But the museum's trustees then issued a statement rejecting Greek demands for the sculptures to be sent back.
The British museum said the talks on 4 May came at a regular meeting between Greek and British government officials, attended also by representatives from the British Museum and the UN cultural organisation Unesco.
On 17 April the Bloomberg news service quoted remarks by British Museum director Neil MacGregor when asked if he would agree to a request from Athens to borrow the marbles.
"There is no reason why an object in the BM, if it is fit to travel, shouldn't spend three months, six months somewhere else." he replied. "So in principle, absolutely yes."
But he added that the Greek government had never asked for a loan - "The issue has always been about the permanent removal of all the Parthenon material in the BM collection to Athens."
The Greeks want to reunite the surviving stones in a new museum
A new museum is being constructed in Athens in which the Greeks wish to reunite the sculptures removed by Lord Elgin with those which remained on the Parthenon temple.
Following Mr MacGregor's remarks, Victoria Solomonidis, cultural counsellor at the Greek embassy in London, said they were "most welcome news" adding: "The Greek side is interested in the reunification of the Parthenon and the issue of ownership does not come into it."
The British Committee for the Reunification of the Parthenon Marbles also welcomed the remarks.
But on 21 April the BM's trustees issued a statement stressing that they saw the sculptures as an integral part of its collection in London, and could not allow the removal of all of them to Athens "even for a short period of time".
"The trustees have lent often to Greece... but they have never received a normal loan request for any of the Parthenon sculptures," the statement went on.
"What successive Greek governments have always sought is the permanent removal of all the sculptures to Athens.
"The trustees do not foresee a situation where they could possibly accede to such a request."
The BM said its representative repeated these points at the meeting on 4 May.
But it said the trustees believed that "friendly discussions continue with Greek colleagues to see if there is any reasonable ground on which a way forward might be constructed".
Unesco's committee on the return and restitution of cultural property is due to meet in Paris on 5-6 June. The Parthenon marbles dispute is always discussed at the meeting's sessions, a Unesco spokeswoman told the BBC News website.
In 2005 the committee invited Unesco's director-general to help organise meetings between the United Kingdom and Greece, "with a view to resolving the question taking in account at the same time the sensitivities of both sides".