The out-of-work German may find himself in demand, with Newcastle and Liverpool both struggling.
According to Sky Bet among others, Liverpool boss Brendan Rodgers is favourite to be the next Premier League manager to leave his post - and Klopp is the bookies' favourite to replace him, just ahead of Carlo Ancelotti.
But Ladbrokes also rank the German as just 7/1 to manage Newcastle next, as detailed in a recent press release.
As Sky Sports have reported, Klopp would be willing to manage a Premier League club as the next step in his career.
But would either Liverpool or Newcastle really interest the 48-year-old? The Reds may be a possibility but reservations have been expressed about whether Klopp would want to work within FSG's strange, ineffective setup.
The Magpies, meanwhile, seem like an even more unrealistic shot. Yet, were owner Mike Ashley and the rest of the Newcastle hierarchy to actually show some ambition and sell the prospect to the German, there is no doubting the St James' Park outfit are a big enough club.