The 21-year-old is a target for Premier League champions Chelsea, who see him as a long-term replacement for the ageing John Terry.
Chelsea, reportedly, have had three bids for the young England international rejected so far and could make a fourth before the transfer deadline expires on Sept. 1.
Martinez reiterated his stance that Stones would not be sold, saying after the Barnsley game that "... in football as in life, money can't buy everything."
"We have not rejected it (the transfer request) yet because today was a match day and that was our priority," the manager said.
"We will reject it in the morning and get on with our business," he added.
"I am not surprised by the request because he is a young man who is under massive pressure from people and outside influences.
"We want to build a winning team and so we want to keep our best performers. John is a big part of our future," the 42-year-old Martinez said.
The manager also refused to criticise Stones for a perceived drop in form against Wednesday night's lower league opponents after his impressive showing in the Premier League since the start of the season.
"For a young man under massive pressure he was terrific," the manager said. "John was just a real example of how to perform under massive, massive pressure and, for me, it was an exceptional display by him.
The Spaniard did, however, repeat his criticism of the transfer window being allowed to stay open past the start of the season, a sore point that has been brought up by several other managers, including West Bromwich Albion's Tony Pulis.
"I am repeating myself but it is wrong for the football authorities to allow the window to remain open when there are important games taking place," Martinez said.
"When there is an opportunity to go to Wembley and to win silverware that should be respected and we shouldn't put our players under this massive pressure."
(Reporting by Simon Jennings in Bengaluru; editing by Sudipto Ganguly)
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