The quartet also includes Chelsea’s multiple trophy winning FA Women's Soccer League (WSL) mentor Emma Hayes, former Italy and Canada coach Carolina Morace, and ex-USWNT assistant Tony Gustavsson.
Football Federation Australia widened the net after two-time FIFA Women’s World Cup winner Ellis told the governing body last month that family commitments in the US precluded her from accepting a contract which runs until 2024.
The most coveted vacancy in the women’s game takes in two Olympic Games, an AFC Asian Cup and, most enticingly, the 2023 Women's World Cup on home soil.
While the process of making a final decision is well advanced, the fact there are no Matildas fixtures scheduled until next March, may delay an official announcement.
Montemurro, whose Arsenal side includes Matildas Caitlin Foord, Steph Catley and Lydia Willians, doesn’t have international experience valued by the FFA board.
But Montemurro, 51, does boast a formidable record at club level - back-to-back W-League titles at Melbourne City and two trophies in his three seasons with the Gunners, including the 2018-19 WSL crown.
His knowledge of the Australian mentality and local landscape are added attributes, not to mention the allure of having a homegrown coach at the helm heading into the co-hosted 2023 showpiece.
Hayes, who brought Matildas goal machine Sam Kerr to the Blues, has won seven trophies in eight years and was most recently linked with the England job, which ultimately went to the Netherlands’ Sarina Wiegman.
As with Montemurro, the 43-year-old one-time Chicago Red Stars coach doesn’t have experience of previous Olympics or World Cups, but her record since taking charge of Chelsea in 2012 is compelling.
Carace, the second female on the shortlist, was a prolific striker for Italy during her playing days.
As a coach, the 56-year-old led Italy to two European Championships during her five years in charge, despite a limited talent pool.
After taking the head coaching role with Canada in 2009, she won four trophies over a two-year stretch, including the 2010 CONCACAF Cup, 2010 and 2011 Cyprus Cups and 2010 Four Nations Tournament.
She had a brief spell as technical director of WA men’s NPL side Floreat Athena in 2015, and is a keen advocate of the Australian game.
Her most recent national team assignment was with Trinidad and Tobago, where things went awry after a pay dispute.
Morace went on to become the inaugural coach of AC Milan women in 2018, finishing the Serie A season in third spot.
The least known contender is Gustavsson, who rode shotgun with Ellis at USWNT for five years and was part of the era which brought World Cup glory in 2016 and 2019.
A journeyman player in his native Sweden, he coached men’s teams Degerfors, Hammarby and Kongsvinger before landing an initial stint with the USA in 2012.
That was followed by two years shaping Tyreso FF into Sweden’s powerhouse women’s team, before Ellis brought him back to the US as her assistant.