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.
"My job is to concentrate on the football aspect, and that is with Celtic," Rodgers said.
"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]."
Rodgers has previously managed in the Premier League with Swansea City and Liverpool, while he has also been linked to the Newcastle United job.
First-team coaches Mike Stowell and Adam Sadler are in temporary charge of Leicester as the club looks for a new boss.