Moody underwent a scan on the Monday and the Rugby Football Union are "optimistic" over his progress ahead of England's World Cup squad announcement on August 22.
But no target date has been set for Moody's return to action by the England medics.
The Bath flanker sustained the injury when Tom Palmer fell on his leg at a lineout, 61 minutes into England's 23-19 World Cup warm-up victory over Wales last Saturday.
Moody was making his international return after missing the Six Nations, having damaged the same knee playing for Bath in January.
England face two more World Cup warm-up fixtures - against Wales this weekend and then Ireland - before their opening World Cup match against Argentina on September 10 in Dunedin.
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