The Reds pair are in contention to win the 2017 edition of France Football magazine's famous prize, which is awarded to the best player over the course of each calendar year.
Coutinho netted a career-best haul of 14 goals last season as Liverpool clinched a return to the Champions League, and has notched three strikes in just six appearances already this term.
Mane was also an instrumental figure for Jürgen Klopp's team in 2016-17 and has brought his good form into the new campaign, scoring three times in all competitions thus far.
Currently held by Cristiano Ronaldo, the Ballon d'Or has been shared between the Real Madrid winger and Barcelona star Lionel Messi since 2008.
Michael Owen remains the only person to scoop the prize during his Anfield stay, doing so in 2001, while Steven Gerrard finished third in the running in 2005.