The Northern Irishman remains adamant that he does not have a new role lined up and is not banging furiously on the door of West Bromwich Albion, still searching for a successor to the Spaniard, Pepe Mel.
He cannot even be pinned down on whether he will return to work, outwith some media engagements at the World Cup finals, in the short or long term. England remains his goal, but Lennon has given little away over the standard of club or competition he regards as the kind of challenge he so desperately seeks after growing tired of the one-horse race otherwise known as the SPFL Premiership.
His trusted assistant Johan Mjallby, who left Parkhead on the final day of the season as his contract expired, is a little more forthcoming. The Swede has given perhaps the most telling insight yet into what his friend, colleague and former team-mate would find attractive and it might prove to be something with a whiff of the unpredictable.
Around a year ago, Lennon was being touted as a contender for the position at Everton, which was, eventually, filled with such aplomb by Roberto Martinez.
Outwith Tottenham Hotspur, known to be fluttering their eyelashes in the direction of Southampton's Argentinian coach Mauricio Pochettino, there are few jobs of that calibre around now.
West Brom could be interesting in the wake of their Premier League survival, but Mjallby believes Lennon would be willing to start his managerial career south of the border with a Championship club waiting to be brought back to life and willing to match his ambitions.
It might take time for such an opportunity to raise its head. It might offer itself in the shape of Brighton & Hove Albion, although their former coach Oscar Garcia, now in the frame for Lennon's old job at Parkhead, cited a perceived lack of investment as one of his reasons for departing in the wake of a play-off semi-final loss to Derby County.
Whether the South Coast club would be the right kind of fit or not, it seems Lennon would not be troubled by the size or reputation of any prospective employer as long as he saw something within the infrastructure to suggest they could both bolster their reputation and worth by achieving success together.
"I definitely think he would consider a top Championship side where he can see he has a chance to really, really make a name for himself and the club," said Mjallby.
"Maybe he could see there is a chance to progress with the team and do something really well.
"We are quite proud of what we achieved and we've put Celtic back on the European map as well. It has not been a poor four years, but you sit down and speak to each other during the season and we both felt it was time for a new challenge.
"It might be together and it might not be, but I am still sad. I didn't really know until a couple of days ago that he was really thinking of leaving Celtic. It was something I had been thinking of for some time and it looks like Neil came to the same conclusion.
"You don't want to get stale in a job. We have done well and improved, but you need to be brave and say that you are getting stale and not improving.
"Even if you go to a lesser team size-wise, you will be working with new players, new challenges and new goals."
Both men enjoyed a good relationship at Celtic Park with the Swede stating that they have come to the collective conclusion that the structure was not in place to make the team truly capable of competing in the European arena.
Celtic have established themselves as a club based upon selling young players for a profit and there is clearly interest in the likes of central defender Virgil van Dijk, whom Mjallby insists should be sold for no less than £8m, and goalkeeper Fraser Forster is widely expected to be sold on before the start of the new campaign.
Mjallby was coy on his own plans when announcing his departure from Celtic earlier in the month, making it clear that reports he was planning to strike out on his own were not necessarily correct.
The fact that Lennon may soon be looking to assemble a coaching staff somewhere or other makes his own situation all the more uncertain.
"This changes things a wee bit," he confessed. "If Neil gets back into it, I am not saying I would expect a call, but we worked well together and I might get the chance to continue working with him.
"If I stay in Sweden, I would be more likely to try as a No.1."
Lennon travelled to Portugal yesterday with a club delegation, including the Lisbon Lions and their families, to take in the Champions League final and admitted managing in England remains his intention despite seeking some private time to recover from his stay at Celtic Park.
"It is an ambition, but I need some time to digest it all," he said.
"Leaving Celtic is a huge wrench and I will probably never leave it in my mind even though I will physically. I have been associated with the club for 13 years and I am sure I will have still a fond association with it. I just need time to think things over.
"I won't rush anything and I don't know if opportunities will come up. People say it is a bit of a gamble, but I just felt the time was right for me and my staff to take our careers in different directions.
"Everyone is speculating about me walking from this job to another, but that is not the case at all."
Lennon also pointed out that his intention of pitting his wits against coaches in England may not be immediately realised. His decision was more about walking away from Celtic when on top.
"It might not be in the short-term," said Lennon. "It might be a long-term thing. I just felt the time was right."