Ronaldo is favoured to scoop the prize after helping Portugal and Real Madrid win the European Championship and Champions League respectively.
Wales talisman Bale and French striker Griezmann also impressed at the Euros, with the latter top scoring at the event with six goals.
Barcelona hitmen Lionel Messi and Luis Suarez are likewise in contention for the accolade.
UEFA explained how the winner will be chosen on August 25 in a statement, which reads: 'Journalists from each of UEFA's 55 member associations provided a list of their five best-ranked players, with the first receiving five points, the second four and so on. The ten players with the most points advance to the second vote, which will determine the three finalists to be named on 5 August.
'The jury will then cast their votes for the outright winner, which will be announced during the 2016/17 UEFA Champions League group stage draw in Monaco on 25 August.'
UEFA's 10-man shortlist:
Gareth Bale (Real Madrid & Wales)
Gianluigi Buffon (Juventus & Italy)
Antoine Griezmann (Atlético Madrid & France)
Toni Kroos (Real Madrid & Germany)
Lionel Messi (Barcelona & Argentina)
Thomas Müller (Bayern München & Germany)
Manuel Neuer (Bayern München & Germany)
Pepe (Real Madrid & Portugal)
Cristiano Ronaldo (Real Madrid & Portugal)
Luis Suárez (Barcelona & Uruguay)