Ellis is the leading contender after guiding the United States to a second Women's World Cup this summer. It was a record fourth triumph for the Americans, while it was the first time they have retained the trophy. Ellis is also the first coach in history to win it more than once.
Neville took England to the semi final of the World Cup, further cementing the Lionesses' status as one of the best international teams in the world. His England team also won the 2019 SheBelieves Cup ahead of the United States back in March.
Montemurro was the coach behind Arsenal's 2018/19 Women's Super League title, the club's long overdue first domestic crown since 2012.
Pedros, meanwhile, led Lyon's continued dominance in France and Europe, with another French Division 1 title, Coupe de France and yet another Champions League win - his second consecutive European triumph and the club's fourth. He has since stepped down.
The other names on the shortlist include Dutch coach Sarina Wiegman, whose team reached a first ever Women's World Cup final this summer, Peter Gerhardsson, whose Sweden side exceeded expectations to finish third at the same tournament.
Italy coach Milena Bertolini is also nominated after taking her country to a first World Cup in 20 years, winning a difficult group and reaching the quarter finals for the first time since 1991.
Japan Under-20 coach Futoshi Ikeda oversaw Under-20 World Cup glory last summer, while Antonia Is guided Spain to victory in the Under-17 World Cup at the end of 2018. Paul Riley won NWSL with North Carolina Courage and was named 2018 NWSL Coach of the Year.
Our first announcement today! #TheBest Women's Coach nominees:— FIFA Women's World Cup (@FIFAWWC) July 31, 2019
gbeng Phil Neville
Voting NOW OPEN https://t.co/MPUnRRrU4Q
Pedros and Wiegman have won the award before in 2018 and 2017 respectively, while German legend Silvia Neid claimed the first when FIFA launched the ceremony in 2016.
Fans can already vote for their top three, with the fan vote equally weighted alongside votes from journalists, national team captains and national team coaches. FIFA's window of consideration for nominees was 25 May 2018 to 7 July 2019 inclusive.
The winner will be announced at the annual FIFA Gala, this year held in Milan on 23 September.