Negotiations are continuing between the former Celtic boss and the Scottish Championship club with a view to him succeeding Alan Stubbs.
Stubbs left for Rotherham United last week after two seasons in charge and having just won the Scottish Cup.
Lennon is believed to want Garry Parker as his number two at Hibs, who missed out promotion to the Premiership after a play-off defeat by Falkirk.
The pair played together at Leicester City and Lennon had Parker as part of his coaching team at Celtic and Bolton Wanderers.
Former Northern Ireland midfielder Lennon, who won the League Cup twice as a player with Leicester, served Celtic as a player for six-and-a-half years, winning five Scottish titles and six domestic cups.
After a spell back in English football, Lennon rejoined Celtic as a coach in 2008 and eventually became manager in 2010.
He enjoyed further success in the dugout at Celtic Park with three successive top-flight titles and two Scottish Cup triumphs before leaving in 2014.
A move to Bolton followed later that year and, although Wanderers initially improved under Lennon, they were bottom of the Championship by the time he left in March, with the side eventually relegated.
Hibs have spent the last two seasons in Scotland's second tier, having also lost out in the promotion play-offs in 2015.
However, having ended their 114-year wait to win the Scottish Cup, the Edinburgh club will enter the Europa League qualifying rounds, with their first match on 14 July.
On Sunday, Stubbs told BBC Scotland he thought that Lennon, his former Celtic team-mate, would be a "a good choice" for the Easter Road vacancy.
Neil Lennon could be appointed Hibernian manager later this week.