Di Santo, who Allardyce signed on loan from Chelsea in the summer to boost his forward line, put in an eye-catching display at Ewood Park last weekend as a 10-man Rovers side came from behind to claim a dramatic late victory over Villa.
The 20-year-old Argentinian is currently on a six-month deal which Allardyce is keen to extend if the opportunity arises in January.
That may not be possible with the transfer ban Chelsea were handed by FIFA last month, but in the meantime Allardyce is keen to see more of the same from the young striker.
"We're never going to keep him at the club (permanently), that was a key thing from the start," he said.
"The best we can hope for is that it is extended to a 12-month loan, but unless they (Chelsea) cover themselves regarding that ban, we think he'll be going back in January.
"It's very important that he continues his progress after the way he played on Saturday against Aston Villa.
"It's important that he continues that progress on a game-to-game basis, that he tries to keep his place in the side, continues to put in those kind of performances and hopefully gets even better. If that is the case it will be very good for us.
"He is keeping out three other strikers at the moment who are not so happy about that. But he took the shirt on Saturday and proved to be very effective for us and we will certainly need him to be in that sort of an aggressive mode against a very good Arsenal side."