The forward would be allowed by the club to resurrect his career at the Spanish side this season.
Premier League sides, Chelsea and Tottenham were linked with a move for the France star until the Premier League transfer window closed against the move.
But with the Spanish transfer window still open until next week, Sevilla are hopeful of landing the player.
Spanish newspaper, Marca reports that the La Liga outfit are still looking to sign an attacker and Martial is on their radar.
The former Europa League winners are also looking at Julian Draxler who is surplus to requirements at Paris Saint-Germain.
The newspaper claimed that Sevilla may only be able to commit to a loan deal.
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