The 25-year-old, capped 18 times by his country, injured his left knee two weeks ago having also missed England's 2013 Six Nations campaign with a different injury on the same knee.
"He is making good progress and we're hopeful another week's recovery and rehab will see him up and running for the Argentina game," England coach Stuart Lancaster told Sky Sports.
"It's a big blow but we've got two very good looseheads in Mako Vunipola and Joe Marler. Joe was one of the pick of our forwards in Argentina and Mako has been outstanding this season so it's a good position for us."
Lancaster added front-row forwards Rob Webber and Henry Thomas to the squad on Sunday as cover for Dylan Hartley (ankle) and David Wilson (calf).
He will announce his team to play the Wallabies on Thursday.
England also play Argentina and New Zealand in November.
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- Disease & Medical Conditions
- Mako Vunipola