The Northern Irishman was suspended by the club last week, along with No.2 Garry Parker, in the aftermath of a heated team meeting at the Capital side’s East Mains training complex.
Lennon’s representatives are understood to have held talks with Hibs’ legal team earlier this week with a view to negotiating a settlement that suits both parties.
The Sun is reporting that discussions centred on agreeing a departure “by mutual consent”.
Academy head of coaching Eddie May and assistant coach Grant Murray took charge of the team for the Ladbrokes Premiership meeting with St Mirren at the Simple Digital Arena last Sunday, which saw Hibs come from a goal down to record a 3-1 win courtesy of goals from Oli Shaw, Darren McGregor and Stevie Mallan.
The duo are expected to continue leading the team for this weekend’s league match with Aberdeen.