The Irishman has not been a manager since leaving Ipswich Town in 2011, but was recently linked the vacancy at Sunderland, another club he has previously managed.
Keane has hinted in the past that he has not given up on management yet and is thought to have dicussed the vacancy at Hibs with his inner circle.
A report by the Irish Independent claims Keane is set to hold talks with the Easter Road club later this week.
Hibs are searching for a new boss after the sacking of Shaun Maloney. He was in charge at Easter Road for just four months.
Club icon David Gray has taken charge of the first team for the remainder of the season.
Ross County boss Malky MacKay was made the early favourite to take over the role on a permanent basis and has held on to his place at the top of the betting market until the reports on Keane emerged.
There have been some other big moves as Kilmarnock boss Derek McInnes has also entered the market and shot up to third favourite.
Meanwhile, David Gray and fellow former Hibs star Kevin Thomson have moved in the opposite direction.
Here are the most recent betting odds on the next permanent manager: