Ronaldo struck the winning spot-kick as Real claimed an 11th Champions League title, beating city rivals Atletico Madrid on penalty kicks in May, before leading his country to Euro 2016 glory.
Fellow Portugal and Real teammate Pepe also featured on the shortlist, along with Wales star Bale.
The former Tottenham Hotspurs star had steered his country to the semi-finals of the European Championship in their first appearance at a major final since 1958.
Ronaldo is favoured to the win the award for a second time, after scooping the honours in 2013-14, which would see him draw level with Barcelona’s Lionel Messi.
Atletico Madrid striker Antoine Griezmann was also nominated after his six goals in Euro 2016 earned him the Player of the Tournament and the Golden Boot.
Unfortunately, France fell short against Portugal in the final match.
The News Agency of Nigeria (NAN) reports that Messi is one of two FC Barcelona players to make the list along with Luis Suarez.
The Bayern Munich duo of Manuel Neuer and Thomas Mueller, Juventus goalkeeper Gianluigi Buffon and Real midfielder Toni Kroos are also included.
NAN reports that the players were selected by journalists from each of UEFA’s 55 member-associations who will vote for a second time on Aug. 5 to determine the three finalists.
The winner of the award will be announced in Monaco on Aug. 25 when the draw for the UEFA Champions League group stage is made.(NAN)