Respected rugby paper Midi Olympique said that games between France and Ireland in Paris and Wales v Scotland in Cardiff were called off by organisers on Monday. The Italy v England game had already been postponed.
A Six Nations spokesperson said that the report, which also said the planned "Super Saturday" finale would now take place on Oct. 31, was speculation.
On Sunday France banned gatherings of more than 1,000 people as the death toll and number of coronavirus infections continued to rise. England, France and Ireland are still in the running for the Six Nations title but it is far from clear how and when the competition will play out.
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Italy's match against Ireland last weekend had also been postponed.
Hosting unions are keen to avoid playing games without spectators as the Six Nations internationals are their biggest income generators, each match earning millions of dollars.
In 2001 the championship held three matches in September and October after they were postponed due to an outbreak of foot and mouth disease. (Reporting by Mitch Phillips/Julien Pretot; Editing by Pritha Sarkar)
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