Arsene Wenger looks under pressure and failure to qualify for the Champions League would surely see his tenure as 'Gunners' boss come to an end.
"I'm loving my life up here. I'm not going to be here forever but I'm living in a dream," Rodgers said.
"Dreams always come to an end at some point, that's for sure. But I am always relaxed about speculation. My focus is only on Celtic.
"Arsenal are a great club, they have a great manager and they are going through a tough time of course.
"People will look at it and see that I went to Liverpool, they were struggling for five seasons for Champions League football and I was able to get them back.
"And when I came to Celtic, they hadn't been in the Champions League for two seasons and I got them back.
Rodgers and his team beat Morton in the cup on Saturday, but all fixtures in the Scottish Premier League were called off due to inclement weather. Next week they go away to Ibrox for the Old Firm game against Rangers.