Borini was left on the substitutes’ bench as Sunderland pick up an impressive 2-0 win over Mark Hughes’ side last week.
Allardyce has hinted that the Italian striker could come back into contention for his team’s match against Arsenal on Saturday, though, with Duncan Watmore also in his thoughts to replace the injured Jermain Defoe.
"Fabio Borini is back and has a chance," Allardyce said. "He was disappointed to be on the bench last week."
Watmore came off the bench to replace Defoe in Sunderland’s match against Stoke, suggesting that he may be the favourite to start at the Emirates Stadium.
The youngster was in impressive form in the Black Cats’ latest outing, and he scored Allardyce’s side’s second goal in the contest.
Borini, meanwhile, has struggled for form since returning to the Stadium of Light this season.
The former Liverpool man has played seven times for the Wearsiders so far, but he is yet to score, and Sunderland have not won a match when he has made an appearance.
Sunderland’s win over Stoke has lifted them out of the relegation zone, and relieved some of the pressure that was on them after their poor start.