The former Celtic and Bolton Wanderers boss had been mulling over a two-year deal, believed to include a significant bonus payment for securing promotion to the Premiership.
Lennon held initial talks with Hibs chief executive Leeann Dempster last Friday and was identified then as the preferred candidate for the vacancy at the Scottish Cup winners.
The 44-year-old, who has been out of work since leaving Bolton in March, had further talks with Hibs yesterday and outlined his wish to bring in his former Leicester City team-mate Garry Parker as his assistant.
It is also believed that Lennon was seeking assurances over the club’s transfer budget before giving Hibs an answer.
Lennon is due to travel to France later this week where he is part of BBC Television’s team of pundits for the Euro 2016 finals.
The Hibs squad are scheduled to return to pre-season training in a fortnight and will face their opening Europa League qualifier on 14 July.
The departure of Stubbs to become Rotherham United manager just over a week after he led Hibs to Scottish Cup glory against Rangers at Hampden reduced the level of euphoria surrounding the club in the aftermath of ending their 114-year hoodoo in the tournament.
But Dempster has promised that the new Hibs manager will be backed financially for a tilt at the Championship title and automatic promotion.
Seeking to build on the feelgood factor generated by the Scottish Cup win, Dempster has written to fans ahead of Friday’s season ticket renewal deadline at Easter Road.
Hibs have sold almost 8,000 season tickets so far, including 1,000 new sales – an encouraging figure according to Dempster. However, around 2,000 season ticket holders from last season have still to renew and Dempster is targeting a final figure of at least 10,000.
“We know you can help us get there to give us the best possible chance of winning the Championship outright and returning to the top flight where this club belongs,” said Dempster.
“The way to do it is to get back to games at Easter Road. Don’t watch from afar, don’t wait for anyone else, just get yourself to Easter Road and support us over the line in 2017. If you can, rally your friends and family to come to games.
“I plan to give our new head coach the means necessary to win the Championship – it is easier to do this with you beside me.
“It is simple, the sooner you can commit to a season ticket, then the more and the sooner we can support our new head coach to get players signed up and prepared for the initial games.
“Life with Hibs has been pretty incredible over the last few weeks. Join us for more next season.
“The [Scottish Cup] win will live long in the life of every Hibernian supporter. It was a fantastic performance and to win in the final minutes of the game was incredible.
“I have spoken to so many supporters. Some young and some older, current season ticket holders and those who are not, and everyone agrees – winning the Scottish Cup gave us all a weekend to remember and a performance to be proud of together.
“In some ways, the victory parade was even more impressive. To have well over 150,000 people line the streets of Edinburgh, dressed in green and white and cheering the team, left me speechless.
“It was a visual representation of the potential of our club. Tens of thousands of people, all touched by our achievement and wanting to join us on that momentous day.
“Now we want to realise that potential on a permanent basis and I really want us to create that togetherness longer term, to be a launchpad for all the things that are already great
about our club.”