Lennon has been installed as manager with John Kennedy his assistant and former Republic of Ireland global Damien Duff promoted to first-team coach after a short stint in charge of the reserves.
Lennon did a fine job in his first spell in charge of Celtic, winning three league titles and having success in Europe.
Former Swansea and Liverpool boss Rodgers has regularly been linked with a return to English football since winning his first Scottish treble and the 46-year-old has recently been touted as a potential successor to Claude Puel should Leicester City decide to part with the Frenchman.
"He is in his dream job, he loves the city, he loves working with the young players and Celtic don't have the finances to go big and spend millions and millions of pounds on new signings".
"Brendan has done ever so well at Celtic over the last few years".
"They push on and wanted to try and push for an equaliser and that's why I am so proud of the team because they showed not just their qualities, their guts, their determination, playing out of position, young players like Ewan Henderson who was brilliant today".
Celtic chief executive Peter Lawwell confirmed to Sky Sports News that the club had spoken to the Northern Irishman.
"Brendan has indicated to the Club that this is an opportunity he wishes to investigate further and therefore, very reluctantly, the Club has granted him permission to speak to Leicester City". "His achievements are historic". We are delighted to also promote John Kennedy to assistant manager and bring Damien Duff into our first-team management group.
"We've spoken to Neil and another couple of candidates".
Celtic are eight points clear of Rangers with the Betfred Cup already in the trophy room and with a William Hill Scottish Cup quarter-final against Hibernian, whom Lennon left in January, to come at Easter Road on Saturday.