Fourth-placed West Ham, who have 27 points from 15 games, have surpassed expectations with a string of fine attacking displays and they will be hoping to record their fourth straight win when they travel to Sunderland on Saturday.
"If we're still here towards the end of January then we'll reassess our aims," Allardyce told a news conference on Thursday.
"By that point we'll have played 20 games, we'll have played everybody once so we should have a good indicator of where we are.
"We'll see what everybody has got in their locker, everybody would've seen what we have in ours so it'll be a question of whether we can carry it on."
England striker Andy Carroll, who missed the start of the season with an ankle injury, struck twice against Swansea City as West Ham cruised to a 3-1 victory.
With fellow forwards Diafra Sakho and Enner Valencia making a seamless transition to the Premier League, Allardyce is delighted with his strike force.
"He's (Carroll) had a long layoff and only played a handful of games. His confidence will get better the more he plays, his goals will help that too," Allardyce said.
"We're the third highest scorers in the League, with nine different scorers before the Swansea game. So we're getting goals from all over the team.
"With our options up front with Valencia and Sakho back as well as Carlton Cole and Mauro Zarate it is a very strong frontline that we can change if and when we need to."
Midfielder Mark Noble is out of West Ham's trip to 14th-placed Sunderland with an Achilles injury and Allardyce expects a tough test from Gus Poyet's side despite the fact they have scored just 13 Premier League goals this season.
"They're hugely difficult at home, playing them away has been tough for us," he said. "They've been struggling for goals recently.
"I think Connor Wickham and Steven Fletcher would've wanted a few more goals than they've got and if they had they would have converted their draws to wins.
"Hopefully, we can keep those guys quiet on Saturday and deliver another good away performance."
(Reporting by Michael Hann, editing by Ed Osmond)
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