Chairman Rod Petrie says it is not vital that Hibernian's new manager is a former player with the Edinburgh club.
Hibs parted company with John Hughes on Monday with his side third bottom of the Scottish Premier League.
And Petrie, speaking at the club's annual meeting, said there was no reason to follow their recent history of appointing former Hibs players.
"Football being football, the telephones, emails and text messages have been red hot," he said.
"There will be a lot of interest in one of the leading jobs in football management in Scotland."
Hibs have had seven permanent managers and in the last 10 years, with the last three - Hughes, Mixu Paatelainen and John Collins - having been former players at Easter Road.
We do not see it as imperative to have a new management team in place for the Kilmarnock game
Hibernian chairman Rod Petrie
And, with assistant manager Brian Rice having also departed, training was supervised on Monday by reserve team coach Gareth Evans, himself a former Hibs striker, goalkeeping coach Scott Thomson and youth coach Alasdair Stevenson.
Evans was assistant at Alloa Athletic and then at Brechin City under Michael O'Neill, the former Hibs midfielder now managing Shamrock Rovers, and both men figure highly with the bookmakers as possible successors.
Jimmy Calderwood, who left Kilmarnock in the summer, is the early bookmakers' favourite along with Ross County's Derek Adams, although many fans have called for the return of former Hibs boss Tony Mowbray.
But Petrie said his board would not be rushed into making a choice and would wait until next week before deciding who would be in temporary charge for the match against Kilmarnock should a permanent appointment still be awaited.
"We have the best part of two clear weeks over the international break to try and make progress," he told more than 200 shareholders attending the meeting.
"We do not see it as imperative to have a new management team in place for the Kilmarnock game.
"We want to take the time to make the right next appointment."
Petrie explained that, following Saturday's 2-0 defeat by St Johnstone, he had spoken to Hughes on Sunday and again on Monday morning.
"Together, we concluded that it would be in the best interests of Hibernian - the club that is so dear to him - for a new management team to take up the reins," he said.
"After a good pre-season, including a four-match tour to Holland with three new signings, we faced the difficulties of an exit from the Europa League to NK Maribor of Slovenia and an exit from the Co-operative Insurance Cup at the first time of asking away to Kilmarnock.
What next for Hibs after Hughes?
"These compound the disappointment felt by being knocked out of the Scottish Cup earlier in the year in the 90th minute of a replay away to Ross County.
"Cup defeats are disappointing, particularly against teams from lower divisions. Cup runs are important to the club, especially in terms of sporting prowess, but also to provide additional income to sustain the development of the club."
Petrie recalled that, after 11 wins in 22 matches, Hibs had made a good start to last season.
"We were to win only four more matches in the final 16 games - the last of those on the final day of the season to clinch fourth spot and a place in the Europa League.
"Despite the changes in playing staff, that poor run of form has continued with just one win in seven league outings this season."
Petrie insisted that the club had given all the support they could to Hughes, despite selling top striker Anthony Stokes to Celtic on transfer deadline day.
"You'll have to trust me it was the right thing to do and the right deal to do at this time," he said.
Petrie nevertheless paid tribute to the effort put into the job by Hughes, who moved to Easter Road from Falkirk 17 months ago.
"John gave of his best and deserves our respect for rising to the challenge and leading the club into Europe," he added.
"It has been a day of emotion and sadness - but it is the right next step for the club."
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