The French star is keen to leave Manchester this summer and Chelsea have become the leading team that might secure his services in the summer.
Alarmed at the inconsistency his club has shown this season, Chelsea owner Roman Abramovich is determined to strengthen his squad in the off-season, although the Telegraph says if they fail to qualify for the Champions League they will be left "facing a shortfall between £50m and £70m".
Apparently the Stamford Bridge outfit are "braced for Real Madrid to firm up their long-standing interest" in their Belgian, and that's spurred them into action vis-a-vis Martial.
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Since Alexis Sanchez's arrival in January, the forward has struggled to get a start in Jose Mourinho's line-up and is said to be considering leaving the club at the end of the season.
Manchester United are still not considering selling the player, but things could change over the next few months. Tottenham and Chelsea are also very interested in the former Monaco man, who has scored a total of eleven goals in all competitions this season.
Last seasons Premier League Champions are attracted to Martial as he can play all across the front-line and also see the France worldwide as a potential replacement for their star attacker Eden Hazard.
Martial's market value is subjected to rise if he performs well at the upcoming 2018 World Cup in Russian Federation.