The Wales international is a target for Premier League club Crystal Palace but Lennon is hopeful he will commit himself to the Hoops' cause.
"I want Joe to stay. We had a conversation on Tuesday. He has intimated that he would like to stay and we are hoping that we can speak to his representatives this week and get that finalised," he said after Ledley scored the winner in Celtic's 1-0 win over Partick Thistle on Wednesday.
"You are never confident, but hopeful. I have spoken to Joe over a number of weeks but it certainly hasn't affected his performances, I thought he was our best player by a considerable margin."
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