However, with Arsenal now on the lookout for a new manager, Rodgers has been linked with the vacancy at the Emirates.
"I made a change eight or nine months ago". It was an ambition to come to here to help the club arrive in the top six.
Leicester came close to levelling in the 54th minute when Ricardo accelerated into the box and forced a one-handed save from Pickford while at the other end Holgate controlled a corner at the back post and hammered a shot from the angle but it was blocked before Mina glanced a headed chance wide from close range.
"I think all the players were so happy for him in there afterwards, as we all are, because there's a lot of guys that are playing regularly, but he's the guy that came into the game today and was the hero for us".
My focus is very much with Leicester. The project feels very exciting with a lot of development ahead.More news: Watford sack manager Flores after 85 days in charge
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Leicester rediscovered their momentum and Iheanacho struck the victor in injury time for his first Premier League goal since September 2018.
Rodgers suggested the contractual clause that enables him to leave under certain conditions is a common arrangement. Most managers' contracts will have something in that but, for me, my only concentration is with Leicester.
Rodgers said he was not bothered by suggestions that Arsenal could try to lure him away.
He continued: "It doesn't annoy me". It's not in my control. The responsibility is to move the club forward and I am very happy trying to do that. I absolutely love it here. Names will get thrown right, left and centre. "With the Arsenal job there is probably about 10 names". "Me, I'm just concentrating on Leicester".
Asked whether he was at Leicester to stay, Rodgers told the BBC 'Yeah, very much so. Rodgers, who took Liverpool to the brink of the title in 2013-14, praised his side's mentality. But nor is he ruling it out. We want to continue with that. I said after the Norwich game you have to show it with actions and they showed that.
His first contribution was to cross for Vardy to tap in the equaliser in the 68th minute, and then he produced a calm finish with his left foot in stoppage time after collecting a pass from Ricardo Pereira.