Chelsea have already failed with two bids for Stones but may yet return with a third for a player also reported to be on the radar of Manchester City and Manchester United.
Martinez, however, insists Everton are not a selling club and not necessarily a smaller one than the current Premier League champions.
Martinez said on Sunday after Duncan Ferguson’s testimonial match: “We feel that we are a big club.
“You’re going to get clubs that are working with big budgets because they have been working in the Champions League, but we are a club with nine league titles, the history and we have just celebrated a big moment.
“We are a big club. What we want is to build and what we want to do is concentrate on the future and we are not a selling club by all means.
“On the outside it seems turmoil and many things happening, but internally John comes in and trains and needs to try earn his place and keep improving, keep taking responsibility in the group and nothing else.
“There is nothing to discuss, he is not a player that is out of contract in ten months, he is not a player we don’t want, he is a player that has a fantastic future with us and there is nothing to comment.”
Stones picked up a knock in the 2-1 defeat to Villarreal at Goodison Park and was substituted with 20 minutes remaining, while Kevin Mirallas went off five minutes before half-time.
Martinez did not seem too concerned about the injuries after the match, however.
“We’ll assess them in the next 48 hours,” he said. “But I don’t expect it to be anything too serious.”
Sunday’s loss followed a 2-0 defeat to Leeds at Elland Road on Saturday, but Martinez is pleased with his side’s preparations for the new campaign nonetheless.
He told Everton’s official website: “It’s been a very good pre-season for us.
“We’ve been working in three environments. The trips to Singapore and Scotland gave us a lot, and being able to work at Finch Farm has been very positive.
“I felt that this weekend stretched the squad to the maximum, so I could make decisions on young players. Following that, I’m delighted with the levels we have.
“Today was also important to see a couple of partnerships and I’m very clear on how we’re going to play next Saturday.”
Martinez has already signed Tom Cleverley and Gerard Deulofeu but added that his summer transfer spending was not finished yet.
“We know we need two to three new players and we are going to make sure we get the right ones,” he said.
“We are looking for that area (attack), the No 10 position, and I think we need a centre-half. The three areas are quite clear.”