The Hoops manager has been heavily linked with the north London club following Arsene Wenger’s announcement that he’ll leave his job after 22 years this summer.
There are others being mentioned, but Rodgers is among the frontrunners due to his impressive form with Celtic over the last two seasons.
But what does he think about the speculation? That’s all it is – speculation, according to the Northern Irishman.
His Celtic team were unable to win and clinch the Scottish Premiership title as Hibs beat them 2-1 at Easter Road.
And speaking to BT Sport afterwards, Rodgers dismissed talk of leaving for Arsenal while reaffirming his loyalty to the Hoops.
Asked for his thoughts on the link, Rodgers said: “Not a lot really – my focus is only on Celtic. At this moment in time, my focus is really just about finishing off this league campaign and obviously we’ve got a Scottish Cup Final to look forward to.
“Like I said before the game, there’s lots of media around now and lots of speculation so there’s nothing to add to that. It’s all speculation and my focus is on Celtic.
“It’s not even a consideration. My focus, as I say, is clearly on Celtic. It’s all hypothetical. I’ve said before, Arsenal is a fantastic club, a great club, but my focus is on Celtic.”
That’s exactly what Celtic fans will want to hear as they go into an important stage of the season.
They still have the league to win after today’s result – and they can do that by beating Rangers next weekend – as well as the Scottish Cup Final against Motherwell, which could give them a double treble.