Nah. Rodgers has never been a serious proposition. Too long remaining on his contract and, right now, he'd be mad to leave Leicester for Spurs. Quite apart from which, he's still seen as too much of a Brenton and a bit of a choker at the (although that might perfectly qualify him for the Spurs job).
Nagelsmann was the main target (and was keen to come) before the Hansi Flick situation at Bayern blew up. Nagelsmann (who is a Bayern fan) is now almost certain to take over from Flick.
Top of the list now appears to be Ten Hag. Rangnick is another possibility - but the idea of him and Levy being able to work together seem very remote. The options drop off rather alarmingly after that, albeit that Graham Potter would be an interesting, if very risky, appointment.