The Barnsley-born defender, who has featured in 16 Premier League matches this season, has made a big impact at Goodison Park in recent months.
It was reported last week that Arsenal boss Arsene Wenger told scouts to run the rule over the defender until the end of the season following his fine performance in Everton's 3-0 win over the Gunners earlier this month.
And now, according to the Daily Mail, Chelsea have joined the race to sign the impressive central defender.
Following the Toffees' 1-0 win over Sunderland on Saturday - a result which leaves the Merseyside outfit fourth in the Premier League table - Everton manager Roberto Martinez hailed the teenager.
“Remember, John is only 19 and Saturday was probably only his ninth game as a centre-half," the Spaniard told Goals on Sunday. "At Barnsley he always played at right-back, but he's got that knack of knowing where to be.
"He's got a really good defensive brain and fantastic defensive intensity - but then he's got the best distribution I've seen in a centre-half."
Everton will be desperate to keep hold of Stones - particularly if they secure Champions League football for next season - while the player is also believed to be happy at Goodison Park.
Stones, though, would face stiff competition for first-team football at both Chelsea and Arsenal, which cost influence his final decision whether to stay or go.