Manchester United parted with an initial £36m to sign Martial, 21, from Monaco in 2015.
But the France international has so far struggled to justify his price tag at Old Trafford.
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He started just 18 Premier League matches last season and only managed to find the back of the net on eight occasions in all competitions.
His future has consequently been the subject of speculation, especially with the Red Devils eyeing moves for the likes of Alvaro Morata and Ivan Perisic this summer.
However The Sun say Martial remains in Mourinho's plans for the future.
But he will apparently only continue to keep faith in the forward if he sees a change of attitude next term.
Martial has two years left to run on his contract with the Red Devils.
Philippe Lamboley, the player's agent, claimed his client was seriously considering a loan move to Sevilla in January.
"We are studying the Sevilla option in detail," he said.
“Sevilla are a very good club, are in a good position in La Liga, play in the Champions League and have a great coach.
"That’s all I can tell you.”
