Borgetti, 32, scored a fabulous equaliser in Thursday night's 1-1 UEFA Cup draw at Besiktas and Allardyce believes he finally has a player who can rival first-choice Kevin Davies for a place in the team.
Allardyce raved: "If Borgetti continues to score like that and play like that, then he's going to force his way into the side.
"That can possibly be Sunday and if not then, I can see it coming on Wednesday against West Ham.
"We've got two games a week all the way into December - and there's the possibility of alternating Kevin Davies if we see a big impact from Jared.
"That'd be great for us and put pressure on Kevin, who's been magnificent for us for the last three years."