Earlier this week, the Dutch prosecutors decided not to begin proceedings to have the men extradited and that they would begin the trial in Romania, DutchNews.nl said.
But the suspects' lawyer, Bogdan Cimbru, said if they are not tried in the Netherlands, the paintings will never be recovered.
"They have made this very clear," Cimbru said.
The suspects do not believe they will get a fair trial in Romania and are worried about spending time in a Romanian prison, DutchNews.nl said. They are looking to make a deal with the prosecutor.
The heist took place on Oct. 16, DutchNews.nl said, and the three men allegedly took works by Monet, Picasso, Matisse and Gauguin.
A 19-year-old Romanian woman is being held on suspicion after possessing the paintings after the robbery, DutchNews.nl said.