"That's likely to be at some point next week. And then the decision will be made on whether that's myself, Chris, or a combination or neither."
Dome revealed the duo would be interviewed as individuals, with Greenacre set to complete the necessary qualifications to be an A-League head coach before the next campaign. And Buckingham felt the two Englishmen had proven their coaching credentials during their time in charge, but were always hamstrung by where they began.
"When we took over, we were bottom of the table with six points," he said. "We're now consolidated in seventh - which isn't where anyone wants to be, but we've taken 24 points [from 18 games].
"The points tally that is now on the board is the second-highest that this football club has had in five years, it's the second-highest goals scored in five years and [ahead of this weekend] it's the second-least goals conceded."
And Dome agreed with Buckingham's assessment of the pair's performance, pointing to recent wins over Newcastle (5-0 without All Whites) and Melbourne Victory (3-0 away) as proof of the current side's potential.
"The existing boys have done more than enough to justify an interview," he told Daniel McHardy on Radio Sport. "We think they did a great job in the time they had to pull together a squad and some of the results they did get.
"But they did just miss out on the finals. I think if they'd gone deep into the finals, it could have perhaps been an easier decision for the board. But, at the moment, they will be considered as part of a wider group."
That group, Dome said, would include multiple applicants from multiple continents, with the process to be overseen by a head coaching committee. The general manager also expressed his desire to have the process completed in "weeks rather than months" and Buckingham concurred that a new boss should be installed as soon as possible.
"Not just for me, personally, but for the players coming off contract," Buckingham said. "If it is myself or if there's another coach coming in, they need time to familiarise themselves with the club and make necessary signings."
Among the men off contract are regular first-teamers Glen Moss, Vince Lia, Louis Fenton, Alex Rodriguez and Roly Bonevacia, the Dutchman who has been heavily linked to signing with Western Sydney.