Chief executive Ben Kensell and head of recruitment Ian Gordon are in London this week for meetings with a number of individuals who have expressed an interest in succeeding Shaun Maloney as the club's head coach.
It is understood that discussions will remain casual at this stage with no formal interviews taking place while the club takes time to weigh up each applicant before producing a final shortlist to take forward.
Hibs are adopting a patient approach after chairman Ron Gordon admitted that the appointment of Maloney was "rushed" having parted company with the first-time boss after just 120 days in charge. Names will be whittled down before interviews are conducted in front of the full board.
Manchester United legend Keane is among those under consideration having made his interest in the role known, with contact established between the Irishman's representatives and the Easter Road club over the weekend.
The former Sunderland and Ipswich Town boss saw his odds plummet from 8/1 to evens with bookmakers yesterday over the prospect of ending his three-year hiatus from the game since quitting his post as Martin O'Neill's assistant manager at Nottingham Forest after just five months in a bid to resurrect his own management career.
Keane, currently working as a pundit with Sky Sports, hasn't held a management role since leaving Portman Road in 2011 but has been an assistant at Aston Villa and the Republic of Ireland national team, as well as his brief stint with Forrest.
Other names linked with the vacancy include Ross County boss Malky Mackay, Kelty Hearts' League Two winning manager Kevin Thomson and Derek McInnes, who led Kilmarnock to the Championship title after taking over in January. Celtic first-team coach John Kennedy has also been considered in the past.
David Gray has been placed in interim charge of first-team affairs and guided Hibs to a 1-0 win at St Mirren on Saturday in the first of their bottom six fixtures.
He is expected to remain in the charge for Hibs’ four remaining games this season against Livingston, Aberdeen, Dundee and St Johnstone on the final day of the campaign.