The former manager stated that if Grealish were to make the step up to England's top-flight, whether it be with Villa or a club like Tottenham, then Grealish might be able to up his game, just like Van Dijk did when he moved from Southampton to Liverpool.
Since playing under more expectations, on a bigger stage and under more pressure, centre-back Van Dijk has taken his game to another level at Anfield - as was proven this season.
Speaking to The Alan Brazil Sports Breakfast Show on TalkSport (14/05/2019 at 8:40 am), Allardyce made the stunning claim that he was unsure Grealish had the legs for top-flight football as he made the Van Dijk comparison.
On whether Grealish will leave if Villa fail in their promotion bid: "It depends on the relationship he has with the owners," Allardyce told TalkSport. "From his point of view, you would think he would want to leave if those attractions are still there.
On whether has the legs for the PL: "I am not so sure. Steve Bruce said he was a terrific player. If he moves to Tottenham, he will up his game. Look at Virgil van Dijk at Southampton. He's completely not the Van Dijk you see at Liverpool. He's a bit more laid back. Made the odd mistake? You don't see anything like that at Liverpool because it brings more out of him.
"I think that'll be the same with Grealish if he were to move to a Tottenham, who were the team that were after him last year."
The Mirror recently reported that Grealish has a £60m release clause in his contract, which will stun potential suitors such as Tottenham Hotspur.
As things stand, Grealish is one game away from making a return to the Premier League with his boyhood club and testing himself against the world's best.
Last season, they were beaten at Wembley by Fulham and those players who were there on that day will want to turn last May's nightmare into this season's dream.
Derby County stand in their way of a return to England's top-flight after they beat Leeds United in one of the greatest games seen in the second tier of English football on Wednesday night.
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