The 25-year old striker has played just four times in the Premier League this season which contributed to him being overlooked for Roy Hodgson's Three Lions squad for next month's friendly with Denmark.
However, Allardyce feels the former Newcastle United and Liverpool forward can use the remainder of the Premier League season to find some form and quite possibly push for a late berth in the squad for Brazil 2014.
"I don't see any reason why he can't make the World Cup squad," Allardyce said.
"It's in his hands what happens between now and the end of the season based upon his performances, when selected.
"After a disrupted first half of the season last season he got into full flow and was selected by Roy Hodgson to go to Brazil.
"Unfortunately, because he was injured in the last game of the season against Reading, he couldn't make that trip.
"If he does the same again then there shouldn't be any problems with Andy being in that final squad for the World Cup.
"He's got to stay fit, perform well and that will give him a great chance of being selected."
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