Everton fell to their eighth defeat of the season but it came in cruel circumstances in stoppage time at the King Power Stadium when Kelechi Iheanacho's goal was eventually ruled as legitimate by VAR.
Rodgers enhanced his reputation even more with a tactical switch that brought a last-gasp 2-1 victory over Everton, with substitute Kelechi Iheanacho creating the equaliser for Jamie Vardy and then scoring the victor in stoppage time.
Rodgers' Leicester side are flying in the Premier League this season, now sitting second after Sunday's dramatic stoppage time win over Everton, and many have suggested he could be the man to succeed Unai Emery.
"Yeah, very much so", he told BBC Radio 5Live. "It doesn't annoy me". It's not in my control.More news: Peru opposition leader Keiko Fujimori walks free from jail
And while managing Arsenal will certainly appeal to him, I would be very surprised to see him make a move to the Emirates.
"I've been very fortunate in my career to work with some brilliant clubs and great institutions". I've loved every minute since I've come here. It seems now you're talking about managers losing their jobs all the time and looking to be replaced.
"Names will get thrown in left, right and centre". For the Arsenal job there are probably about 10 names. Most managers contracts will have something in that but, for me, my only concentration is with Leicester.
Things came together perfectly for Everton midway through the first period, though, when Richarlison started a move by finding Calvert-Lewin who moved the ball on to Iwobi and his perfectly-weighted ball for Sidibé down the right allowed the Frenchman to swing in a teasing ball that the Brazilian powered home.
He has now scored in six straight Premier League games, halfway to breaking his own record for goals in consecutive matches.More news: Centurion Yasir Shah reveals the longer he batted, the easier it became
It left Everton 17th and boss Silva insisted his future was out of his hands.
"I think he'll be disappointed he never got the Chelsea job, he'll have got one eye on what's happening at Manchester United. Tomorrow will be another day for me to prepare another training session".
Silva said: "I never had doubts about that".
"For me, at this moment, we've had a brilliant win today. It was hard in the first half, they sat in but we tried to stay positive and play our offensive game", he said.More news: Donald Trump faces two impeachment deadlines as inquiry shifts focus