Rodgers took charge of the Foxes on February 26 and he has managed to guide the 2015/16 Premier League champions to second in the table, eight points behind one of his former employers, Liverpool.
It looked like Leicester were going to slip 10 points adrift of the leaders when being held 1-1 at home to Everton on Sunday afternoon, only for substitute Kelechi Iheanacho to score a 94th-minute winner.
Celebrations were on hold initially after the linesman raised his flag for offside but, after a VAR check, the goal was rightly awarded, resulting in wild scenes at King Power Stadium as the hosts picked up a 2-1 victory.
What was very apparent was how all the players and coaching staff mobbed manager Rodgers on the sidelines when the goal was given, a sign that they are keen for the Northern Irishman to stay in the East Midlands.
Reports are claiming Arsenal, who recently sacked Unai Emery, want the Leicester boss to take charge at Emirates Stadium and oversee a complete overhaul of the squad.
The Gunners drew 2-2 at Norwich City on Saturday with Freddie Ljungberg in temporary charge and it looks unlikely the latter will be given the job permanently due to his lack of managerial experience.
Rodgers was quizzed about the speculation after the Everton victory, and, although eluding to a potential clause in his contract, he insists he is happy at the King Power.
"It was an ambition to come here to help the club arrive in the top six. Everything's been great since we've worked together," he told Sky Sports. "My ambition is to help this club, a responsibility to share that with the others and move the club forward.
"There's great potential here at Leicester City to push on in the next few years."
Leicester return to action on Wednesday when they host rock-bottom Watford, who sacked manager Quique Sanchez Flores on Sunday after just 85 days in charge.