Khazri, a £9million capture from Bordeaux, made an impressive debut as a half-time substitute in the Black Cats' 1-0 home defeat by Manchester City on Tuesday evening, showing flashes of the talent in which the club invested so heavily.
Allardyce was reluctant to pile the pressure on the 24-year-old Tunisia international by comparing him to Frenchman Djorkaeff and Nigerian Okocha, both of whom he described as "world-class", but the 61-year-old is hoping he can have a similar impact on Wearside as they did in Bolton's rise to Barclays Premier League prominence.
He said: "You are going world-class now, man
I'm not sure he's world-class - if he is, it will be the bargain buy of the century.
"One of our problems is we get to the final third fine - we arrived in the final third much more than Manchester City, we produced more in the penalty area than Manchester City did against us - but our quality is the ultimate [problem] in that area.
"It's the hardest place to produce that quality, so if he's got that quality in the final third which helps us provide and score more goals, then he'll be a massive bonus to us - as in the past Youri Djorkaeff particularly, in a similar position, and Jay-Jay Okocha provided in my Bolton time."
Khazri could make his first start in Saturday's trip to Liverpool, although Allardyce could be forgiven for not wanting to change the team which played so well in narrow defeat by City.
He lined up wide on the right in midweek, but has the versatility to perform several roles.
Asked where he sees Khazri playing his football, Allardyce said: "Left or right mainly, or on the frontline if we need him.
"But in the main, he is just happy to play where we pick him with a big smile on his face, which is nice to see because with our Christmas and New Year, it's been a long haul for the players to get through that, whereas the four new players who have come in come in smiling every day because they are where they want to be.
"And where they want to be is where? In the Premier League."
Khazri, defender Lamine Kone, midfielder Jan Kirchhoff and striker Dame N'Doye all played a part on Tuesday night, a day after the winter transfer window closed with Scotland international Steven Fletcher's loan move to Marseille the most notable of a series of departures.
Allardyce said: "It was a big decision that was made by both of us, but really in the end, he wasn't happy about the fact he hadn't played the last few games, didn't feel that he was going to get back in and so on that basis, I didn't want him hanging around moping and griping and feeling sorry for himself.
"I took the decision on the fact we have got Dame N'Doye, we have got Jermain Defoe, we have got young Duncan Watmore, we have got Wahbi who can all play up on the frontline, so I still think I have got plenty of choices in those areas."
Source : PA
Source: PA