The duo have been eclipsed by Real Madrid's Luka Modric and a phalanx of French players who were key to the country's surge to the 2018 World Cup in Russia.
Zinedine Zidane was the last Frenchman to claim the award. That was in 1998 following France's World Cup victory.
Strikers Kylian Mbappé and Antoine Griezmann lead the charge with midfielders Paul Pogba and N'Golo Kanté also in the fray. Raphael Varane and Hugo Lloris - from the team's rearguard - are also in the mix for the award which will be announced on Monday night in Paris.
Modric was at the heart of the Croatia team that battled its way to the World Cup final. The 33-year-old was also instrumental in the Real Madrid that notched up an unprecedented third consecutive Champions League crown.
"Modric is an exceptional player. He has shown that throughout his career, not just at Real but also at his former clubs and with his country," said Real coach Santiago Solari.
Even if Mbappé does not join the likes of Alfredo Di Stefano, Joahn Cruyff and Marco van Basten, this year, he is expected to lift the trophy at some point in the next few seasons.
However, the teenager is likely to win one bauble - the Kopa Trophy. Decided by 33 living former Ballon d'Or winners, it will be given to the best player aged under 21.
Mbappé has underlined his credentials with match winning performances on the way to the World Cup final and a goal in the showdown against Croatia.