Rodgers is one of a number of managers to have been linked with the soon-to-be-vacant post as the Gunners prepare for life after Wenger, who will end his 22-year reign at the club this summer.
However, the former Liverpool boss - who saw his side claim a seventh consecutive Scottish title courtesy of a 5-0 drubbing of Old Firm rivals Rangers yesterday - insists that he is already in "the best job in the world".
"It's the longest shortlist I've ever seen! I woke up here on a Monday morning as the manager of Celtic, and I'm in the best job in the world. Believe it or not the sky is blue here in Glasgow, I absolutely love it here," Rodgers told talkSPORT.
"I've got huge respect for Arsenal as a club. When I started my coaching career Arsene was just coming into the club and I learned so much in that period as a young coach watching him, so it's a club I've got huge respect for. But I'm so happy here at Celtic. I'm in a job I love, it's a huge club with big expectancy and big pressure.
"I would love to work in the Premier League again one day, but I'm hopefully going to coaching for another 20-odd years. The board has been so supportive of me here and, from the first day I walked in, the supporters have given me everything. I feel a loyalty to them to ensure we keep moving the club forward and keep progressing."
Celtic could wrap up a historic double-treble when they take on Motherwell in the Scottish FA Cup final next month.