The Argentine striker has been heavily linked with a move away from Juve this summer and he admitted last week that he would love to play in the Premier League.
According to La Gazzetta dello Sport, Allegri is already considering replacements in the event of Higuains departure and has identified Martial as the 30-year-olds long-term successor in attack.
The report also claims that Allegri has Chelsea striker Alvaro Morata on his shortlist if Juventus are unable to sign Martial.
La Gazzetta dello Sports report on Monday claims that Allegri has informed Juventus of his two choices to replace Higuain, while Robert Lewandowski and Edinson Cavani are not top of his shortlist because they are of a similar age to the Argentine striker.
Martials future at United remains uncertain after a difficult season under Jose Mourinho.
The 22-year-old missed out on a place in Frances World Cup squad and struggled for regular playing time following Alexis Sanchezs arrival from Arsenal in the January transfer window.
Reports have already claimed that Mourinho has given the green light for United to sell Martial this summer.
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