Ronaldo – the winner in each of the last two years – and Modric both starred for Real Madrid as the Spanish giants won the Champions League for the third year running, while the latter also won the Golden Ball for the best player at the World Cup after inspiring Croatia on their run to the final.
Meanwhile, Egyptian star Salah scored 10 times as Liverpool made it to the Champions League final, before losing 3-1 to Real in Kiev.
Salah was forced off with a shoulder injury in the first half of that game after a clash with Real defender Sergio Ramos.
He also netted 32 goals in his debut Premier League season, with that tally a record for a 38-game campaign.
Lionel Messi came fifth in the voting by a jury of 80 coaches from clubs who played in the Champions League and Europa League, as well as 55 journalists representing each UEFA member nation.
The Barcelona star came second to Ronaldo last year but also failed to make the final three-man shortlist in 2016.
Atletico Madrid’s France star Antoine Griezmann, who scored twice as his club beat Marseille 3-0 in the Europa League final, just missed out in fourth.
The winner will be named, along with the UEFA Women’s Player of the Year, in Monaco on Thursday, August 30, the same day as the draw for the Champions League group stage.
The nominees for the women’s award are France’s Amandine Henry and Norway’s Ada Hegerberg, who both won the Champions League with Lyon, and Denmark’s Pernille Harder, who lost in the final with Wolfsburg.