The 42-year-old has been linked with newly-relegated Championship side Norwich City for some time, but recent reports emerged claiming that Lennon could move to Premier League outfit West Bromwich Albion.
While the Northern Irishman has constantly denied contact with another club, the coach has maintained ambitions to manage in England's top flight.
According to the Daily Record, the decision was made by Lennon purely because he wants a new challenge as opposed to any issues with the club's hierarchy.
The former club captain took control at Parkhead in 2010 and led Celtic to three league titles and two Scottish Cups during his time in charge.
Lennon's former Celtic teammate Henrik Larsson is reportedly the bookmakers' favourite to take the job.