Ronaldo helped his former team Real Madrid win three UCL titles on a bounce - to bring their tally to 13 in the history of the championship.
Modric, who reached the World Cup final with Croatia after picking up the Champions League with Real Madrid at the end of last season, is aiming to break up a decade-long duopoly.
Luka Modric, Ronaldo and Mohamed Salah will be competing for the best player honour.
Ronaldo scored 44 goals in all competitions in his final season for Real Madrid, while Salah netted the same amount for Liverpool in 52 games, while also breaking the Premier League record for most goals in a 38-game season with 32.
However, if he does win, the the Portugal star won't be there in person to collect the award as he will miss the ceremony at London's Royal Festival Hall due to commitments with club team Juventus.
Messi's solitary World Cup goal against Nigeria and Ronaldo's spectacular overhead kick against his future employers in the Champions League quarter-finals are two of 10 goals on the shortlist, also including Gareth Bale's acrobatic strike for Real in the Champions League final.
The best goalkeeper award will be fought for between Thibaut Courtois, Kasper Schmeichel and Hugo Lloris.
Lyon's Reynald Pedros won women's coach of the year, Peru fans won the FIFA fan award, the FIFA Fair Play honor was given to former VVV-Venlo striker Lennart Thy, and Brazil's Marta was named the female player of the year.