Wenger is set to leave the Emirates Stadium after 22 years in charge and speculation surrounding his successor is growing.
Ex-Liverpool boss Rodgers is one of those the Gunners are said to be interested in hiring to succeed their long-term coach.
However, having just won his second Scottish Premiership title with Celtic after a 5-0 home win over Rangers on Sunday, the Northern Irish manager says he is completely happy in Glasgow.
“I woke up here on a Monday morning as the manager of Celtic, and I’m in the best job in the world," he told Talksport. "Believe it or not the sky is blue here in Glasgow, I absolutely love it here.
“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 be 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.”
After winning three trophies with Celtic last season, Rodgers can make it a back-to-back treble when they take on Motherwell in the Scottish Cup final on May 19.