The 42-year-old former club captain stepped down on Thursday having led the club to three Scottish Premiership titles during his four-year spell in charge.
Lennon has been linked with a number of jobs south of the border but insisted he had nothing in place as he left Glasgow.
Asked for his future plans, Lennon said on Sky Sports News: "I've no idea
A holiday, hopefully
I'm away with the club tomorrow for the Champions League final and then I'll take the family away for a bit of R & R."
While his immediate future remains unclear, Lennon said he made the decision to leave Parkhead after careful consideration.
"I think it's a really good time to go," he said
"The club's in great health and I just felt that, after long consideration, four years as a manager of Celtic in a very intense atmosphere has been fantastic for me
I never dreamt when I took over the job I'd be in this position now.
"There's been a lot of consideration
This is not a knee-jerk reaction
It's been going on for a while and it's the toughest decision of my life."
Lennon has said he will help Celtic chief executive Peter Lawwell pick the man to replace him.
In a statement released earlier in the day, Lennon said: "Serving the club was always a privilege
I have always given my best and aimed to do all I can to ensure success for Celtic, as a supporter it was all I wanted.
"I will now assist the club in appointing my successor
As ever, we will need our fans' support and I am sure they will give the club and the new manager the same great backing which they gave to myself."
Former Hoops idol Henrik Larsson has been installed as the bookmakers' favourite, but there is backing too for fellow Parkhead old boys Malky Mackay and Paul Lambert
But while the bookies seem convinced Larsson will be the next man to take over at 'Paradise', the Swede played down the suggestions
The retired striker - now in charge of Falkenberg in his homeland - told the Daily Record: "I understand that I always will be linked with the job in Celtic after my years in the club as a player
"Of course I can see myself as manager of Celtic and to go there in the future
But my focus now is on Falkenberg
Nothing else."
Lennon replaced Tony Mowbray in March 2010 as caretaker after the Englishman's disastrous reign ended with a 4-0 thumping at St Mirren
He was given the job permanently despite losing a Scottish Cup semi-final to First Division Ross County just three games into his temporary stint in charge.
The Northern Irishman's first full season also ended in disappointment as Rangers snatched the title, but at the end of that campaign he told the Parkhead crowd: "This is not the end, it's just the beginning."
Since then, Lennon's team has reigned supreme on the domestic front with three league wins in a row
There was success in Europe too as Lennon's team stormed to the knock-out stages of the Champions League last year - a run that included a famous Parkhead win over Barcelona.
But the former Leicester City midfielder now looks certain for a return to England after growing frustrated that his attempts turn the club into a European power were hampered by their lack of financial might in the transfer market.
As well as his three league wins as boss - which made him just the fourth Celtic manager to land three in a row after Willie Maley, Jock Stein and Gordon Strachan - there was also two Scottish Cup triumphs during his reign
However, controversy has never strayed far from Lennon during his time in Scotland.
He was given a four-match touchline ban following a spat with then Ibrox assistant manager Ally McCoist back in March 2011.
That same month, a parcel bomb addressed to the Celtic boss was intercepted by Royal Mail staff
Two men were later jailed after being found guilty of conspiring to assault Lennon and two other victims.
Lennon was also attacked in the dug-out at Tynecastle in May of that year after a supporter leapt from the Hearts end and charged straight for him.
Despite those ugly incidents, Lennon insisted he had enjoyed his time in Glasgow's east end.
"I have supported Celtic all my life and the club will always be part of me," he said
"I t was an absolute honour to play for this great club , to captain the team and of course to become Celtic manager , a position which I cherished dearly
However, I feel the time is now right to move on to a new challenge."
Source : PA
Source: PA