Blues manager Jose Mourinho is said to view the 21-year-old as the long-term replacement for captain John Terry and is prepared to spend big to lure him to Stamford Bridge.
Stones, who was signed by David Moyes from Barnsley for £3m in 2013, is under contract until 2019 and has remained silent on the speculation linking him with a move away from Merseyside.
Roberto Martinez declined to comment about the saga when he was quizzed after the 3-1 pre-season friendly victory over Hearts on Sunday.
"We always try to look for new arrivals and I feel we are looking for two positions to try to strengthen, but it is a good period to assess the younger players," he said.
The Spaniard sees Stones, who has four England caps to his name, as a future Everton captain and would prefer to strengthen his backline rather than lose a vital component of it.
Having allowed Antolin Alcaraz and Sylvain Distin to leave the club this summer, the Toffees need reinforcements before the Premier League curtain-raiser against Watford on 8th August.
"It’s always important in the way that we work at our football club, that we assess our youngsters before we make major decisions," Martinez added.
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"I've been very impressed with their attitude and levels, and we’ll keep working until the deadline day to try and be as strong as we can be as a squad.
"At the moment with where we are, we’re trying to have that consistency in our group. We’ve been working really hard in the last two seasons to do that, I think we've got a very good balance in experience and young talent that they already have big roles in the team and we want to maintain that, and if anything add extra strength to our strong core that we have."