Journalist Kerstin Hasenbichler reported from Valencia that the potential 2013 ban is being discussed as part of the sport's cost-cutting efforts.
The teams and the FIA are "currently in consultation to restructure regulations aimed at keeping costs as low as possible", the writer said.
A tyre blanket ban was considered a few years ago but shelved on safety grounds.
It would, however, save money both on equipment expenditure and freight costs.
Pirelli's Paul Hembery confirmed he would "welcome" the ban but warned it "would require a complete change of the composition" of the tyres.
He said the ban should therefore be introduced over two years.
For 2013, Hembery said, warmers for wet tyres could be banned, preceding a full ban for slicks the following season.