The England midfielder has scored six goals and registered three assists since in eight matches since joining the Hammers on loan from Manchester United in January.
Bruno Fernandes, a £47million arrival from Sporting Lisbon last January, had a similar impact in the second half of the Premier League campaign with eight goals and seven assists in 14 appearances.
It led to discussions among fans over whether Fernandes should have been a contender for the PFA Player of the Year award, which was eventually won by Man City playmaker Kevin De Bruyne.
And Cascarino reckons the same talks should be had about Lingard, who has helped West Ham into the top four since arriving in east London.
He said: "If you go back to last season, Fernandes came to Manchester United in January.
"He played half a season and then there was the debate over whether he should be a candidate for Player of the Season.
"A lot of fans, probably mostly United fans, felt that with how big of an impact he had. It's made me think, could you make the same argument for Jesse at West Ham?
"Could he be a candidate for Player of the Season?"
Meanwhile, talkSPORT host Simon Jordan reckons Manchester United could demand £60million for Lingard this summer.
He said: "I just don't see where there is a parallel universe where they're going to get Lingard to West Ham or they're going to get the economics of the Lingard deal to West Ham.
"What West Ham have achieved is putting Lingard back on the map, giving Lingard a stage where he can play at the level that clearly he's capable of.
"All that will do is increase the cost implications of getting him in the first place.
"[If Lingard wants to join West Ham permanently] what Manchester United will say is, 'that's great, you can go there if you want to, that's £60m.'"
Jesse Lingard could be a Player of the Year contender if he maintains his form for West Ham, according to Tony Cascarino.