Reports claim the Northern Irishman is interesting the midlands club who are searching for a replacement for Steve Bruce.
The former Swansea and Liverpool boss, who has guided the Hoops to back-to-back domestic trebles, recently revealed he had rejected overtures from a Chinese club in the summer.
After the 6-0 win over St Johnstone at McDiarmid Park in the Ladbrokes Premiership, Celtic boss Rodgers was asked about the Villa rumours and said: “I have been linked with a number of things and I’m sure that when clubs need a manager there is always a raft of names mentioned.
“It is a huge club, a Premier League club, great facilities as I said it before when John McGinn (Celtic target) was going.
“Brilliant support base, big history, but I am sure they will know who they want to go in there.
“I have a great job here, a very exciting challenge this season and I am loving every second of it.
“So yeah, you can’t rule me out because I have never been asked.”