Leicester now sit second in the table, one place about Manchester City.
Rodgers appeared to scoff at claims that he had practically invited Arsenal to inquire about him when he confirmed in a television interview that he has a clause in his contract allowing him to talk to any club willing to pay a potential release fee.
After previously missing out on his signature when he was at Celtic, the Gunners may live to regret not taking their chance on Rodgers when they had the opportunity.
He told BBC Radio Five Live: "He's playing a game".
"If the people at Arsenal have moved Unai on, I'm sure they have an idea of who they want to bring in". "I don't think so much about it".
Many Leicester fans had given up on the Nigerian after he struggled to make any sort of impression in his stay at the King Power Stadium thus far, but some are left changing their mind about the attacker after this display.
"They will have been conversations with his representatives".
Rodgers said of the rumours regarding the position at the Emirates: "I have a contract here until 2022". If you are not trying to throw a little bit of incitement out there, just say "it is personal contract issues".
It would be a significant blow to Leicester if Rodgers was to jump ship but it would also be a surprise move, given the start to the season his side has made. It was the ambition to come here and help the club to rank among the top six. I'm working with a group of talented players. I don't want to see the manager sacked.
"But it's all about happiness and I couldn't be happier here".
He said: 'I'm not the right person to ask about that.
"I gave an honest answer, which was based around probably most managers have something in their contracts, and by all accounts that "opened the door" for something".
"I thought his first-half performance was very very good, I thought Marco Silva got a tune out of his team and performance from his team, and I think Sidibé was a shining light in that". We still have a lot of work to do.
"We're moving to a new training facility".
"For me, I repeat, I'm happy here, very happy and have great relations with all the people and I feel I want to continue with that".
"I think the position he is in, there is no doubt you want to get right to the top", he said.