Keane won seven Premier League titles, four FA Cups, and the Champions League in his 13 seasons at Old Trafford.
Neville was alongside Keane for much of that success and the pundit feels Alli can adapt his game to be a top class central midfielder.
“What I would say on Dele Alli is, in my view he will evolve, he will change, I think he could end up in central midfield," Neville said on Sky Sports' Monday Night Football show.
"I think he could end up controlling the game, I think he could end up being a good passer of the ball.
Gary Neville is big fan of Dele Alli and compared him to Roy Keane (Image: GETTY)
“I think his mentality is fantastic and his hunger is brilliant.
"So you think about first to the tackle, second balls, things that would be the ugly side of the game, Dele Alli can do that.
"Obviously he'll need to develop and understand how to defend more because he's played further forward at the moment.
"I think he's a flexible football player that will evolve over his career and will end up with the ability to go back deeper.
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Dele Alli scores his Tottenham's second goal (Image: GETTY)
"Look, Roy Keane is the most influential player I ever played with but I think Dele Alli has got that in him.
"In the early years of 21, 22, you sort of look at that if he develops as he is doing under Mauricio Pochettino,
"I see no bounds of where he could end up.
"Some of the greatest midfield players of the last ten or fifteen years, Steven Gerrard or Paul Scholes or Roy Keane, they ended up being a lot deeper as their career, they would charge into the box every time."