The nominees were revealed on the Premier League’s official website on Friday.
The other three players also on the shortlist are Caglar Soyuncu of Leicester, Raul Jimenez of Wolverhampton Wanderers and Sheffield United’s Lys Mousset.
Mane was a recipient of the Player of the Month award in March this year, while Vardy is the current holder after emerging winner for October.
Fans can have their say on who wins by voting on the EA SPORTS website before 18:00 GMT on Monday 9 December.
The fans’ votes will be combined with those of the 20 club captains plus a panel of football experts to determine the winner.
And for Barclay’s Manager of the Month award, four coaches were shortlisted.
The managers are Nuno Espirito Santo of Wolves, Jurgen Klopp of Liverpool, Leicester’s Brendan Rodgers and Chris Wilder of Sheffield.
Fans’ votes will be combined with those of a panel of football experts to decide November’s winner.
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