And reports subsequently emerged suggesting the Foxes would be prepared to wait until the end of the season to get the Celtic boss, who is the early odds-on favourite to land the job.
However, Rodgers, who has won seven major trophies in under three years with Celtic, was not willing to entertain speculation ahead of the 4-1 Scottish Premiership home win over Motherwell on Sunday.
"My job is to concentrate on the football aspect, and that is with Celtic," Rodgers told BBC Scotland.
"I've been stood here for two-and-a-half years and I've been asked similar questions. My message is always very, very clear: I'm very concentrated on the game.
"We're in really good form and my concentration is fully on getting the three points [against Motherwell]."
First-team coaches Mike Stowell and Adam Sadler are in temporary charge of Leicester as the club look for a new boss.