Manchester City striker Aguero has scored 23 goals so far in 2014 despite missing chunks through injury, while Rooney has netted 20 and his Manchester United team-mate Van Persie has notched 17
Former Liverpool forward Luis Suarez was also omitted.
No English players made the list, but Wales and Real Madrid forward Gareth Bale was included along with Manchester City trio Vincent Kompany, Pablo Zabaleta and Yaya Toure.
Chelsea duo Thibaut Courtois and Diego Costa are also on the list, as is Manchester United's Angel di Maria and Arsenal's Alexis Sanchez, although all of them were playing in Spain's Primera Division last season.
Bundesliga giants Bayern Munich can boast nine members of their squad - Manuel Neuer, David Alaba, Medhi Benatia, Jerome Boateng, Philipp Lahm, Xabi Alonso, Arjen Robben, Thomas Muller and Robert Lewandowski have all been nominated.
European champions Real Madrid, meanwhile, have eight members of their squad with Cristiano Ronaldo, Karim Benzema, Luka Modric, Toni Kroos, James Rodriguez, Sergio Ramos and Dani Carvajal joining Bale on the list.
The 40 players have been chosen by UEFA.com writers based on their performances for a European club or national side during 2014
The public can select their preferred formation before picking their starting XI from four goalkeepers, 12 defenders, 12 midfielders and 12 forwards.
Shortlist for 2014 UEFA Team of the Year:
Goalkeepers: Manuel Neuer (Bayern), Thibaut Courtois (Chelsea), Gianluigi Buffon (Juventus), Beto (Sevilla).
Defenders: Sergio Ramos (Real Madrid), Diego Godin (Atletico Madrid), Miranda (Atletico Madrid), Vincent Kompany (Manchester City), Jerome Boateng (Bayern Munich), Medhi Benatia (Bayern Munich), David Alaba (Bayern Munich), Ezequiel Garay (Zenit St Petersburg), Mats Hummels (Borussia Dortmund), Philipp Lahm (Bayern Munich), Pablo Zabaleta (Manchester City), Dani Carvajal (Real Madrid).
Midfielders: Toni Kroos (Real Madrid), Luka Modric (Real Madrid), Angel di Maria (Manchester United), Arjen Robben (Bayern Munich), Ivan Rakitic (Barcelona), James Rodriguez (Real Madrid), Koke (Atletico Madrid), Xabi Alonso (Real Madrid), Marco Reus (Borussia Dortmund), Paul Pogba (Juventus), Yaya Toure (Manchester City), Arda Turan (Atletico Madrid).
Attackers: Gareth Bale (Real Madrid), Diego Costa (Chelsea), Thomas Muller (Bayern Munich), Cristiano Ronaldo (Real Madrid), Zlatan Ibrahimovic (Paris St Germain), Robert Lewandowski (Bayern Munich), Alexis Sanchez (Arsenal), Karim Benzema (Real Madrid), Lionel Messi (Barcelona), Jonathan Soriano (Salzburg), Carlos Tevez (Juventus), Neymar (Barcelona).
Source : PA
Source: PA