Campbell, whose absence was felt in Arsenal's 5-3 win over Middlesbrough on Sunday, has an Achilles problem that will also rule him out of England's World Cup qualifiers in Austria on September 4 and Poland four days later.
"I am in good shape," he told Sky Sports on Sunday. "It is coming along and hopefully it will be another three weeks.
"I need at least 10 days to two weeks' pre-season work, but it is good."
Manager Arsene Wenger said Campbell would train for the first time on Monday and indicated the central defender could be back for Arsenal's first Champions League group game on September 14 or 15, for which the draw has yet to be made.
Wenger said that skipper Patrick Vieira, who is out with a thigh injury, would be back in one or two weeks' time.
