There's an AP piece which suggests the Getty's director is recommending the Getty return some antiquities (from PE.com):

The Getty Museum's director has agreed to recommend the return of some of the four ancient artifacts wanted by Greece that are currently housed in the Los Angeles museum.

Getty Museum director Michael Brand and Greek Culture Minister Giorgos Voulgarakis said Tuesday in a joint statement after meeting in Athens that Brand would make the recommendation to the Getty's Board of Trustees.

The statement did not specify which of the artifacts a gold wreath, a 6th Century B.C. marble statue of a young woman, a votive relief and a funerary slab would be mentioned, and no further details were given.

Greece claims the objects are among thousands of antiquities believed to have been illegally exported as part of a booming trade in the country's priceless archaeological heritage.

"In establishing the framework of a good relationship between the Hellenic Ministry of Culture and the J Paul Getty Museum, it was agreed that the representatives will recommend to the Board of Trustees of the Museum the return of some of the claimed antiquities in the near future," Brand said, reading from the statement.

"Talks are ongoing and representatives will be appointed to seek resolution of the matter within the next two or three months," Brand said.

"Once the requirements of the Ministry of Culture are met, a fruitful cooperation, which could include long-term loans, can start," the statement added.

Brand did not elaborate on the nature of any possible long-term loans.

Asked if he had been pressured into making this decision, he replied: "No."

The BBC coverage adds some details, inter alia:

No details of which of the items may find their way back to Greece have been revealed.

Museum director Michael Brand met with Greek officials in Athens, where he agreed to suggest to his board of trustees that items be returned.

He said handing back the artefacts could lead to a "fruitful co-operation" between the countries which could include long-term loans of museum pieces.

Now here's what I don't understand: all this going-after-museums stuff is supposed to have an effect on looting and make the world safe for provenance, yadda yadda yadda. Can someone explain to me how that works? Near as I can tell, all that's happening here is that museums are going to be taken out of the group of potential customers, so purloined stuff is just going to end up in the hands of private collectors where we'll NEVER see it. And with the shrinking market, those collectors will be operating in a lower price regime, which will take even more antiquities 'out of circulation'.