“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."
The players did not look shaken by the news as they ran out easy winners in a feisty game against Steve Robinson’s men.
Keeper Bain explained as much afterwards, saying: “[The speculation] isn't really unsettling.
Claude Puel was sacked by Leicester on Sunday morning (Image: Getty)
He's got a contract here. There's nothing much that we can do, we'd love him to stay.
Scott Bain
"We've got a group of players here that have shown how focused we are over the last few years and what we are capable of.
“So I think we're all just coming in and we're all just as focused as normal, and go on to do the best for the club as always.”
Rodgers has a contract with Celtic until June 2021, but Bain did admit the coach’s decision is out of the players’ hands.
"He's got a contract here,” Bain added, before saying, “there's nothing much that we can do, we'd love him to stay.
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Brendan Rodgers was confronted with questions about the Leicester job before Celtic's win on Sunday (Image: Getty)