Allardyce is determined to take things one step at a time with the Irons' marquee summer signing.
"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 will be joining us in Germany, and hopefully he will be available, as will George McCarthy, as quickly as possible," the West Ham manager said.
"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.
"If we are going to put our lads through six weeks of preparation and then Andy gets fit with two days to go, you would not expect us to play him, would you?"