Faletau missed the autumn internationals after breaking his arm playing for Bath in the Premiership in October.
The 28-year-old returned to action for his club in an 18-16 Champions Cup victory over Wasps on Saturday, but the BBC reported that he had suffered another break and would be out for around eight weeks.
Wales kick off their Six Nations campaign away to France in Paris on Feb. 1.
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An eight-week absence would give Faletau a slim chance of returning for Wales' final match at home to Ireland on March 16.
(Reporting by Toby Davis; Editing by xxx)
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