The stars are judged on their displays in all competitions, at domestic, continental and global level.
Modric won the Golden Ball for captaining Croatia to the final, where his team lost to France.
With Mohammed Salah and Luka Modric making up the three-man short-list, the pair also played in the UEFA Champions League, although Modric was also named the Golden Ball victor in this summer's World Cup in Russian Federation.
Modric was once again instrumental in steering Madrid to the Champions League crown for the fourth time in the past five years, and built on that display by winning the Golden Ball award at this summer's World Cup in Russian Federation.
Ronaldo, now with Juventus, has won the UEFA award each time Madrid has been European champion since the vote was introduced in 2011. Messi was fifth in this year's voting, UEFA said Monday. Ronaldo was also instrumental in the Champions League, finding the back of the net 15 times in 13 appearances as Los Blancos went on to lift a third consecutive title.
The vote does not always reward a Champions League victor. Messi and Barca also won the Copa De Rey, so Messi would be well within his rights to be a bit miffed for his shortlist omission.
Varane is on an all-Madrid defenders list with Marcelo and Sergio Ramos, and the goalkeeper candidates are Alisson, Gianluigi Buffon and Keylor Navas.
Mo Salah has been nominated for the UEFA men's player of the year award, but there is no place on the shortlist for Lionel Messi. He is joined by Atletico teammate Diego Godin and Dimitri Payet of Marseille.
Pernille Harder, Ada Hegerberg and Amandine Henry are on the women's shortlist.