The Bhoys boss feels that the former Arsenal and West Ham United star can follow the lead of his ex-Sweden teammate Henrik Larsson and become the man to take Celtic back to the summit of Scottish football.
"Henrik came here a few weeks ago and you could see what a good player he still is. Freddie has put down that marker in training too. I think it would be fair to say we need that kind of experience," Lennon said.
"That was not a short-term thing, that was development for the next few years.
"But you also want a couple of kings in the team that can talk others through it at times and we just lack that."
Ljungberg and Celtic are currently in talks regarding a deal and Lennon hopes it comes through as the midfielder, who has spent the past two years in the USA with Seattle Sounders and Chicago Fire, would bring plenty to the Hoops squad.
"He would bring experience and he might bring a calmness to the team as well. You could see in training he was quite willing to talk to the younger players," he added.
"Experience and a bit of quality as well is what he would bring. The one thing we are lacking is that bit of nous. There is no doubt about that."