The emergence in leadership qualities of Greene has placed some pressure on Coniglio, with some suggesting the Giants forward be elevated from his vice-captain duties.
Greater Western Sydney's football hierarchy are set to make a call on the captaincy as early as this week, according to 7 News' Tom Browne.
"Giants footy bosses will decide on the captaincy as early as Friday," Browne reported on Tuesday.
— 7NEWS Melbourne (@7NewsMelbourne) December 7, 2021
"Stephen Coniglio battled with form this year, that was well documented. Sources say the highly regard captain will most likely retain the role."
Browne put light to the fact that Greene will miss the opening five matches of the 2022 season following his extended suspension for making contact with umpire Matt Stevic in the Giants' elimination final win over Sydney in August.
Despite this, Greene and Kelly are understood to have been among the leading candidates to join potentially be appointed as captain at GWS following a player survey within the club.
"Toby Greene and Josh Kelly polled well I'm told in a recent player survey," Browne added. "Keeping in mind, Greene is suspended for the first five games.
"They're weighing up one, two or three captains."
Both Greene and Kelly were members of the Giants' leadership group this year, with Greene appointed as Coniglio's right-hand man, while Kelly, Lachie Whitfield and Matt de Boer also took on roles in the group.