Last year, the sport's new official tyre supplier used defunct team Toyota's updated 2009 car - driven by Nick Heidfeld, Pedro de la Rosa, Romain Grosjean and Lucas di Grassi - to develop its P-Zero tyres.
But according to motor sport director Paul Hembery, the TF109 has been sent back to Toyota's Cologne headquarters because it is now too old.
Finland's Turun Sanomat reports that Hembery has scheduled to discuss a new solution at the next meeting of the F1 Commission late next month.
The newspaper said Hembery wants the teams to release a 2011-spec car for Pirelli to test throughout this season.
"We don't have an agreement yet," he said. "We do simulation (work) but to do the kind of development we need to do, we also need to drive quickly on a track."
Turun Sanomat said a stumbling block at the moment is the fracturing of the teams' association FOTA.