The 32-year-old started West Ham's opening-day defeat to Tottenham last month, but suffered the injury in training shortly afterwards and has not featured since.
Ahead of his side's trip to Manchester United in the Premier League on Saturday, Allardyce confirmed that Nolan was back among the squad, although he will not be available for the clash at Old Trafford.
"Kevin Nolan is training today for the first time, he won't be included for the squad against Manchester United," he said in a press conference on Thursday.
"Same with Matt Jarvis. There's an Under-21 game on Monday they'll probably play a part of.
"It's good to have those two players back in full training, so that leaves Andy Carroll, [Cheikhou] Kouyate and Joey O'Brien out, hopefully not for long."
Kouyate is out for up to six weeks with a groin injury suffered in last weekend's 3-1 win over Liverpool, while Carroll remains absent after having surgery on an ankle problem.
And Allardyce believes the former Liverpool man could be out for another two months.
"We don't want to put a time on it, it might be sooner but we don't want to rush him back," he said. "It all depends how the rehabilitation goes.
"We have to be ultra-careful and if we feel an extra week will do him good then that's what we'll do.
"When he's back hopefully he'll be back for good. We can only guess at a day for when he'll be back. In and around late-November or early-December I think."
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