The trust that operates the Los Angeles museum has returned three artworks but the fate of 21 other pieces, including a prized statue of Aphrodite, remains unresolved, the Los Angeles Times reported on Saturday.
Francesco Rutelli, Italy's culture minister said last month that six months of negotiations over the return of the items had stalled.
"I'm afraid the process of conciliation will end and a serious conflict will begin," he told the LA Times in a statement on Friday.
"The negotiations haven't made a single step forward," Giuseppe Proietti, a senior cultural official, told the Times in a recent interview.
"We will not accept partial solutions. I will suggest the Italian government take cultural sanctions against the Getty, suspending all cultural cooperation."
That could include working with Italian institutions on research, cultural studies, excavations, exhibits or artwork loans.
Getty officials said they still hoped for an agreement.
"My sense is that wisdom and reason will reign here, and the two sides, Italy and the Getty, will find a way to get past whatever problems exist in the short term," Ron Hartwig, the Getty's spokesman, said.
The museum has clashed with Italian and Greek officials over allegations that former antiquities curator Marion True knowingly received dozens of archaeological treasures between 1986 and the late 1990s that were stolen from private collections or dug up illicitly.
True and American art dealer Robert Hecht are on trial in Rome, accused of trafficking in stolen artifacts. They deny wrongdoing and the Getty trust continues to pay for True's defence.