The Wales international, like Georgios Samaras, is in the last few months of his deal with their respective futures subject to much speculation.
In the 39th minute of the Scottish Premiership clash with Partick at Parkhead, Ledley showed why his manager is so keen to keep him by driving in from 25 yards for the only goal of the game, extending the Hoops' unbeaten league run to 19 games.
Afterwards, Lennon said: "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.
"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.
"Joe has showed great mental strength, it must be a very unsettling period for him and for Georgios as well.
"Joe has been an important player for me and the club and he gives us stability.
"You can't have all the players leaving for big money, or bringing in players to develop for a couple of years.
"I need a spine to stay together, the likes of Scott Brown, Ledley, Kris Commons, Samaras - if we can get him - and a few others, because they have been big players for us."
On Samaras, linked with a move to Hull, Lennon said: "Again, we need to speak to his representatives and see how the land lies.
"It is an unsettling period for him and he is a little bit insecure on things so we need to try to endeavour to get him happy again.
"I think he would like to stay but whether we can strike a deal or not is another thing. As far as I know there is interest from other clubs."
It was Celtic's third successive win by the same result to keep them 11 points clear of second-placed Motherwell.
Lennon, though, admitted his side were "flat" and in desperate need of their break in Turkey which will come after the game against St Mirren on Sunday.
The Northern Irishman said: "We lacked spark, particularly in the final third. There were some good bits of play but I and the supporters expect better.
"That's two our of the last three games we have been flat and it looked like things are catching up with us. We need this break.
"We looked heavy-legged and mentally tired. We also need an injection of new blood. There is no question that the squad needs freshening up and we will endeavour to do that.
"It needs a jag as we are starting to look laboured in our play but it was a win, we need to take the positives from that."
Partick boss Alan Archibald claimed his side should have been awarded a penalty in the second half when Ledley tangled with Christie Elliott inside the Hoops box, only for referee Kevin Clancy to take no action.
Archibald, who thought his side "deserved something, at least a point" said: "I didn't know at the time he was in the box but I thought it was a foul and I didn't know why he didn't give it.
"But I know now, it was in the box and that is why he didn't give it here. I am not surprised by that. Anywhere else on the pitch it is a foul.
"It is one of those ones you would say was a soft penalty but it was definitely a push, it was clear to see."