FIFA's official YouTube channel might also show the live coverage of the Ballon d'Or ceremony.
Also on Monday, Mbappe was named the first-ever victor of the Kopa Trophy as the world's best under-21 player.
The annual football award, presented by France Football, has been dominated by Messi and Ronaldo for the past decade, with each clinching the accolade five times apiece since 2008.
Apart from Ronaldo, Modric and Antoinne Griezmann makes the three man shortlist for the prize this year - leaving Barcelona's Lionel Messi out of the equation.
After 13 games, the Old Lady have won 12 and drawn just one, leaving them eight points ahead of second-placed Napoli.
Speaking after picking up the award, Modric said: "It is a unique feeling".
The 33-year-old has already lost two major awards to his former teammate Luka Modric earlier this year.
France worldwide and Paris Saint-Germain striker Kylian Mbappe has won the inaugural Kopa Trophy for the best Under-21 player.
Modric helped Croatia reached the final of the 2018 FIFA World Cup during the summer.
If Modric does indeed lift the trophy, it will be the first time since 2007 - when Kaka won the award - that it has not gone to Messi or Ronaldo.