Lennon is now on loan at Everton but the former Liverpool defender envisioned his career going a little differently to how it eventually unfolded at Spurs.
The 27-year-old could still have a future at Tottenham but, for now, is an Everton man.
And Carragher is certainly, or at least was, a fan of Lennon's ability when he trained with him at the World Cup in 2006:
"I trained with him at the World Cup in 2006 and thought he was going to become a star," he said in the Mail.
In the short term, meanwhile, Carragher feels the Tottenham-owned winger could make the difference for Everton late on in this evening's Merseyside derby against Liverpool.
Lennon will provide somewhat of an unknown quantity when it comes Liverpool - Everton clashes and the former Reds defender believes Roberto Martinez could utilise his pace in the latter stages of the clash.
He added: "I make Liverpool favourites and they have momentum after a number of good results. But they are certainly not odds-on to win and maybe Lennon’s speed will be a weapon that Martinez can use to full advantage late on."
Everton host Liverpool at 5.30pm today, while Lennon's parent club Tottenham host Arsenal at 12.30pm at White Hart Lane.
Everton will stay 12th should they beat Liverpool, although the Reds can potentially leapfrog Spurs into sixth if they win and the north London side don't pick up any points against the Gunners.