The England striker, who completed a permanent £15m move from Liverpool to the Hammers last month, is still recovering from a heel injury and has so far missed the club's pre-season campaign which continued with a 2-1 win at Colchester on Tuesday.
There were suggestions that Carroll could be fit for the Premier League opener against Cardiff on August 17, but that appears unlikely according to Allardyce, who is still hoping to have the 24-year-old back before the international break at the start of September.
Speaking after the match at Colchester, Allardyce said: "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.
"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?"
The win at Colchester gave West Ham a fourth successive pre-season friendly success and Allardyce has been encouraged by their form.
He added: "It was a good workout for us, because Colchester are a couple of weeks ahead of where we are with their season starting earlier, so you would expect we would get a physical game.
"Our only disappointment was conceding a goal in the last minute.
"We are looking very good, even at this early stage, so I just hope we can keep it up in Germany."