The stunning development could see Rodgers walk out on Celtic with them eight points clear at the top of the Scottish Premiership, with the club looking to claim an eighth consecutive top-flight title.
A club statement read: “Celtic Football Club today confirmed that it has been approached by Leicester City FC to speak to Brendan Rodgers with regards to their current managerial vacancy.
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.”
Rodgers is set to be joined at the King Power Stadium by his assistant coaches Kolo Toure, the former Arsenal and Manchester City defender, as well as coaches Chris Davies and Glenn Driscoll.
Furthermore, Celtic are understood to be ready to appoint former midfielder and manager Neil Lennon as caretaker manager until the end of the season, five years after he left Celtic Park at the end of the 2013/14 season.
Leicester are understood to have approached Rodgers on Monday in an effort to make a swift appointment for Puel’s replacement, having sacked the Frenchman after the weekend’s 4-1 home defeat by Crystal Palace.
Rodgers is set to return to the Premier League for the first time since being sacked by Liverpool in October 2015, having won back-to-back Premiership titles with Celtic since replacing Ronny Deila for the start of the 2016/17 campaign.
If appointed, Rodgers will be tasked with lifting Leicester City up the Premier League table after Saturday’s heavy defeat left them down in 12th place.
Puel issued a statement through the League Managers’ Association on Monday to thank Leicester for his time at the club and pay tribute to the late owner, Vichai Srivaddhanaprabha, by speaking of his “honour” to have been given the opportunity to manage the side.
“I would like to thank everyone that I worked with at Leicester City Football Club,” Puel said. “It was a privilege to work with the players, the staff and the management.
“It was my honour to work for the late and much loved Khun Vichai, who gave me the fantastic opportunity to manage his club and share some great moments with him.
“My mission at Leicester City Football Club ends here but I will continue to follow the performances of the team and wish the club all the best for the future.”