Allardyce feels the big frontman can force himself into Roy Hodgson's squad for the summer showpiece in Brazil if he can recapture the form shown towards the end of last season.
"I don't see any reason why not, apart from the fact that it's in his hands with what happens between now and the end of the season based upon his performances when selected," Allardyce said.
"After a disruptive first half of the season last season he got into full flow and I think he scored seven goals in 12 games and got selected by Roy Hodgson to go to Brazil.
"Unfortunately because he got 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 Brazil.
"He's got to stay fit, perform well and that will give him a great chance of being selected."
For breaking stories and all the great banter like us on Facebook: facebook.com/tribalfootball