Rodgers has been touted as a long-term replacement for Unai Emery after the Gunners parted company with the Spaniard last week.
The Northern Irishman has propelled Leicester to second in the Premier League and Sunday's dramatic come-from-behind win to beat Everton has only enhanced his managerial credentials.
Speaking after the game, Rodgers distanced himself between the speculation about Arsenal wanting him [Team Talk].
But Keys once shared a taxi with 46-year-old, and the former Sky presenter is certain that the Foxes manager would listen to what's on offer in North London.
He wrote: "I’ve mentioned my taxi ride with him before. He was with us here at beINSPORTS after losing his job at Liverpool.
"I won’t go into detail, but during the journey back to his hotel, he left me with absolutely no doubt that Arsenal’s was the job he coveted, but he had to be careful how he got there."
It's worth pointing out that the conversation Keys is referring to happened after Rodgers was sacked by Liverpool, which was over four years ago.
So it's very plausible that the Leicester coach - who won seven out of seven domestic trophies at Celtic - might have had a change of heart in his image of Arsenal.
The hotseat at the Emirates isn't as attractive now as it was in 2015, when Arsene Wenger was there, so City fans need not worry a great deal about Keys's taxi ride with him.
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