Martial has endured a difficult season at Manchester United since Jose Mourinho's appointment last summer.
The 21-year-old scored 17 goals as the club won the FA Cup under Louis van Gaal last term.
But he has found life under Mourinho tricky, scoring just three Premier League goals.
Sevilla were backed to move for him back in December and rumours over a summer transfer have refused to go away.
Anthony Martial is determined to stay at Manchester United
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Anthony Martial impressed under Louis van Gaal last season
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But Martial is determined to stay at United, and has praised their supporters for their unwavering faith in him.
“For me, what’s really special here is the supporters," he told Inside United.
"They’ve been really outstanding with me.
"I think that’s what goes a long way to making me feel at home and at ease, and makes me really keen to stay here at the club.
Anthony Martial has found life tough under Jose Mourinho
“In France, even if you’re one of the best players around, they might begin to boo and jeer you if you go a couple of games without scoring.
"But here it’s just the opposite, they’ll try to cheer you on so you might be able to score, and so then you grow in confidence.
“I think it’s just a different mentality. That’s why I like the fans here so much.”