Kris Commons has revealed it is the target for the players, who are now top of the Premiership table after their 2-0 win over Motherwell coincided with Inverness crashing 4-0 against St Johnstone.
The reigning champions' record reads won seven and drawn one, and they are the only side in the division to have avoided defeat this term.
However, only once in their 125-year history have the Hoops managed to go an entire season unbeaten. That was way back in 1897-98 when they only had to play 18 games, winning 15 of them.
Four times since have they lost only once, 1916-17, still under Willie Maley, 67-68, under Jock Stein during their nine-a-row-years, 95-96, when they still finished second to Rangers, and, most recently, 01-02, when Lennon was part of Martin O'Neill's championship team.
So the Celtic boss knows just how tough it is to achieve this.
And Lennon is wary of allowing this kind of talk to gain any strength, mindful of the fact that, prior to the bitterly disappointing defeat to Morton in the League Cup, a treble was subject on the lips of so many.
The Parkhead boss said: "People were asking me about the treble a couple of weeks ago. So, it (talk of an unbeaten campaign) is all very premature.
"But I'm delighted with the start to the season we have made in the league, and with the football we are playing.
"We've set the players targets in the league, and they are achieving them so far."
Lennon admitted climbing to the top of the table for the first time this season was one target already achieved.
And the manner in which they overtook long-time leaders, Inverness, made it all the sweeter.
"It means a lot, even at this stage, psychologically," said Lennon of claiming first place.
"All round, it was a great day for us on Saturday, with us beating Motherwell, Inverness losing to St Johnstone and Aberdeen losing to Ross County.
"It gives us a gap at the top and a cushion with the game we have in hand, as well.
"Our goal difference has also improved, so it was a very satisfying day."
It was also Celtic's first clean sheet in seven games across three different competitions, and news of this delighted the Parkhead manager.
"I didn't know that," he admitted. "We started off the season well in terms of clean sheets, so it was important to get back to that on Saturday.
"There is no doubt that, with the onset of the Champions League and the demands those games bring, there is a fatigue that sets in around 10-15 minutes before the end of matches.
"But, with the extra day of recovery we had from playing on the Tuesday rather than the Wednesday, there was a better freshness about us overall."
The one disappointment was the shoulder injury to Adam Matthews after he landed awkwardly following a challenge from Keith Lasley.
The Welsh international will see a specialist today, but Lennon fears he will be ruled out of action until the turn of the year.
"Adam landed really badly on his shoulder," said the manager. "It could be a fractured collarbone which could see him out for quite a considerable period of time."19