Real Madrid won La Liga, the UEFA Champions League and the FIFA Club World Cup under Zidane last season, while Mourinho claimed three trophies in his first term with Manchester United and Conte steered Chelsea to the Premier League title.
Manchester City boss Pep Guardiola is also nominated, despite failing to win a trophy last term, along with Atletico Madrid's Diego Simeone and Juventus' double-winning specialist Massimiliano Allegri.
Germany manager Joachim Low is included after his side's FIFA Confederations Cup triumph, while Brazil boss Tite is a more surprising name in the running for the award last won by Claudio Ranieri.
Monaco coach Leonardo Jardim earns a place after their Ligue 1 title triumph and run to the Champions League semi-finals, but Paris Saint-Germain boss Unai Emery misses out.
The 12-man list was composed by a panel of former stars including Cafu, Diego Maradona, Carles Puyol and Edwin van der Sar.
A final trio of nominees will now be decided by a combination of a public vote, which runs between August 21 and September 7, as well as input from national team captains, coaches and a panel of media representatives.
SHORTLIST IN FULL:
Massimiliano Allegri (Juventus)
Carlo Ancelotti (Bayern Munich)
Antonio Conte (Chelsea)
Luis Enrique (Unattached, at Barcelona in 2016-17)
Pep Guardiola (Manchester City)
Leonardo Jardim (Monaco)
Joachim Low (Germany)
Jose Mourinho (Manchester United)
Mauricio Pochettino (Tottenham)
Diego Simeone (Atletico Madrid)
Zinedine Zidane (Real Madrid)