With the mid-season transfer window now open, reports have suggested that the Merseyside club would be willing to part with the talented England international.
A price tag of £45 million for the 21-year-old has been mooted, with defending Premier League champions Manchester City viewed as potential suitors for Barkley's services.
However, Martinez is adamant that the club have not received an approach for Barkley and has no desire to allow him to exit Goodison Park.
Speaking ahead of Tuesday's FA Cup third round tie with West Ham, Martinez said: "We haven't [received an approach].
"This January window it's vital that we concentrate on recapturing our best moment of form and start building a good momentum in our season.
"All of our best performers, even if they get a lot of attraction from the outside and they get a lot of compliments, there's not going to be any of them going in January.
"I really enjoy watching Ross. He's one of those players with real passion for the game, that enjoys playing football. You would always pay a good entrance fee to watch Ross."
While Martinez is unwilling to allow any departures in January, he revealed Everton are exploring the possibility of signing a goalkeeper with Tim Howard out fot six weeks due to a calf problem.
Martinez added: "We're looking into that position to see if we can take it any further. There a couple options that I can feel could fit in really well but we're not bringing in someone just for the sake of it."
Defender John Stones is available to feature against West Ham after picking up an ankle injury against Stoke City on Boxing Day, but James McCarthy will miss the tie with a hamstring issue.
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