The Everton defender has enjoyed an impressive few months at Goodison Park, taking advantage of Phil Jagielka’s absence through injury to establish himself in Roberto Martinez’s team.
And former Three Lions and Toffees striker Lineker believes the 19-year-old would be worthy of a spot in Roy Hodgson’s provisional squad, which will be named on Monday.
Watch Stones being interviewed ahead of the U20 World Cup last summer
"The only one I might take a chance on, because we are so short in central defence, is Stones," revealed Lineker.
"I really like him, and he has got a lot about him."
The former Barnsley youngster has enjoyed a real rise to prominence, since moving to Everton from his hometown club last January.
He only made his international debut for Noel Blake’s U19s in September 2012 and was part of the squad for last summer’s U20 World Cup in Turkey, so already has experience of a big tournament.
Lineker has backed John Stones for the World Cup squad
And he has been one of the best performers in Gareth Southgate’s Under-21s this season, helping them to top their Euro qualifying group so Lineker believes he's deserving of a chance.
"Is he worth a gamble? Well, if Roy loses another one - if Jones doesn't make it for example - then what else have we got?" he added.
"Sometimes central defenders need a little bit more experience than players in other positions because of the extra discipline and the nature of that particular role.
"We have got Cahill and Jagielka, then Caulker, who struggles a little bit on the turn. We are short in that position."
