Funes Mori left the field on a stretcher clutching his left knee after 36 minutes as Argentina lost 2-0 to Bolivia in a World Cup qualifier in La Paz on Tuesday.
He has made 26 appearances for Everton this season and would have been in Everton manager Ronald Koeman's plans for the lunchtime kickoff at Anfield.
The international break has not been kind to Everton's defence with Seamus Coleman breaking his leg while playing for Ireland against Wales last Friday.
Everton have not commented on the severity of Funes Mori's injury but it seems unlikely he will be fit.
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(Reporting by Martyn Herman, editing by Ed Osmond)
