Lennon wants the 29-year-old striker to return to Easter Road for a third spell, having been released by Blackburn Rovers this summer.
"The club have done everything they can," Lennon told BBC Radio Scotland.
"It's a purely personal decision for Anthony, but we have a board meeting on Monday, so hopefully we will hear [from Stokes] before then."
Stokes left Hibs to join Lennon's Celtic squad in 2010 and was loaned back to the Edinburgh side in 2016.
Capped nine times by the Republic of Ireland, the forward has netted 131 goals at club level - including two against Rangers in Hibs' 2016 Scottish Cup final win.
"I have had private chats with Anthony, I met him on Wednesday and the talks were positive," explained Lennon.
"But he has a lot of offers and has a big decision to make at this juncture in his career.
"If he decides to come to Hibs, it won't be for the money, even though it is a very good financial package.
"From a footballing point of view, I think this is his home. He has had a great time here in two previous spells.
"He hasn't played a lot of football in the last two or three years and his conditioning would need a bit of work, but I think he is at his peak.
"The [Premiership] season starts next week and we can't wait forever."
Hibernian head coach Neil Lennon hopes to hear by early next week if Anthony Stokes will be rejoining the club.