Chelsea had a 20 million pounds offer for the versatile defender, who made his England debut last year rejected by Everton on Friday, British media reported.
But the Premier League champions were expected to bid again.
Martinez, talking after a 3-1 defeat by Arsenal in the final of the Premier League's Asia Trophy in Singapore on Saturday, said further bids for the 21-year-old former Barnsley defender would not be welcomed.
"We pride ourselves on playing a certain way and educating our young players in a manner that they are going to always get attention from elsewhere and that is always a compliment," the Spaniard told reporters.
"The other side is the disappointment of seeing a football club leaking such statements to the press and making it so open.
"That is not the way we would do it at Everton, we would not speak of a player who is registered at another club and there is no issue from our point of view - John Stones is an Everton player."
Pressed again on the issue and the likelihood of further bids from Chelsea, a visibly irritated Martinez offered a firm reply.
"We are not a selling club," said the coach who won the FA Cup with Wigan Athletic in 2013.
"We are not a club that needs to be worried about what other clubs put through the press."
(Editing by Julian Linden)
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