"Neil has already enjoyed a hugely successful spell as manager of Celtic and, of course, served the club with distinction as player and captain over so many years", said Celtic in a statement. "For us, we just see how that pans out really".
"When we appointed Brendan we knew we were bringing someone of the highest standard to Celtic".
"But Celtic fans will say that Celtic is the club and he's let them down".
Brendan Rodgers has verbally agreed to become Leicester City's new manager and could be installed before Tuesday night's kick-off against Brighton, Sky Sports News understands. Rodgers also completed the first of two domestic trebles as he lifted the Scottish Cup and Scottish League Cup, repeating the feat in 2017-18. He has been a tremendous ambassador for Celtic and I wish him every success for the future. The 2011-12 season saw Lennon recover from a poor start, which at one stage placed his job in jeopardy as Celtic fell 15 points behind Rangers. With the Scottish Premiership title sealed alongside the Scottish Cup and League Cup crowns in his first two seasons, the current campaign was always about the never-before-achieved treble treble for the Hoops.More news: Colombian leader orders humanitarian convoy to return
However, Brighton's alarming slide towards the bottom three continued as they could not find an equaliser and now have not won in seven league games.
Rodgers has already won two league titles in Scotland since being named manager in the summer of 2016.
The Northern Irishman was confirmed as boss just an hour before kick-off at the King Power Stadium, with Mike Stowell and Adam Sadler in caretaker charge.
Newcastle are headed in the other direction as once again they were inspired by the performance of record signing Miguel Almiron to end Burnley's eight-game unbeaten Premier League run.