Martial has endured a frustrating season at Manchester United under Jose Mourinho.
The France international blossomed under Louis van Gaal last term, scoring 17 goals across all competitions.
However, he has managed to find the net just seven times this campaign.
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Tottenham reportedly want to sign Manchester United striker Anthony Martial
Anthony Martial scored as Manchester United beat Watford on Saturday
Sevilla and Paris Saint-Germain have both been backed to rescue him from his Old Trafford nightmare.
But The Mirror claim Tottenham are planning to gazump their rivals with a shock summer swoop.
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Spurs believes a deal could be struck should United sign Atletico Madrid striker Antoine Griezmann.
Tottenham wanted to sign Anthony Martial during his time at Monaco
Manager Mauricio Pochettino is a known admirer of Martial and tried to sign him before United back in the summer of 2015.
Martial faces a fight to save his United career despite scoring in their 2-0 win over Watford on Saturday.
Mourinho has been publicly critical of the 21-year-old, with various reports claiming he could offload Martial at the end of the season.