The Northern Irishman is among those to have been mooted as a possible target for the Championship club following their decision to part with Steve Bruce.
He told BBC Scotland after overseeing a 6-0 victory for his current employers over St. Johnstone: "I'm the Celtic manager and I love it and have lots of challenges here.
"There is always speculation around lots of names.
"Villa is a top Premier League club in the Championship and I'm sure with their support base and resources they will try and get back there as quickly as they can."
Rodgers recently admitted to having received several offers to leave Celtic during his reign at Parkhead.
He has never entered into any talks, with a lucrative approach from China among those to have been knocked back.
"Since I have been at Celtic I have had a few offers, " Rodgers said in September amid an uncharacteristically slow start starting to the 2018-19 campaign for the Hoops.
"So [China] is no different to any of the others.
"My focus is very much on Celtic, trying to help us rise to the challenge of this season.
"What you know with China is it's an awful lot of money, big money, but I have found happiness here. I spoke to the owners of the club and the board and we find an agreement and move on.
"I have had other opportunities but I am very much here, I have this year and two more years on my contract.
"Unless they get fed up with me or something else happens I am very privileged to be here."