The England international has missed the Hammers' pre-season campaign so far with a heel injury after he completed a reported £15m move from Liverpool in June.
Allardyce told Sky Sports News: "Andy is still recovering. He has got four weeks or more to go before he starts full training.
"His rehab is going pretty well at the moment and he will be joining us in Germany, and hopefully he will be available, as will George McCarthy, as quickly as possible.
"I hope it will be before (September) for both of them, but being fit and being ready to play are two different things - they may be fit from the injury, but they are unlikely to be capable of playing straight away."
West Ham's pre-season continued with a 2-1 win over Colchester United.