Just months after leaving the Reds, Klopp has been named head of soccer for Red Bull.
Writing in his column for the Sunday Mirror, Fowler said: "Once football gets in your blood you are hooked.
"That’s why I wasn’t surprised to hear that Jurgen Klopp had returned to the game just four months after admitting that he just didn’t have the energy to carry on as Liverpool manager. I knew Jurgen would be back - and sooner rather than later.
"One thing that did cross my mind when Klopp’s appointment with Red Bull was announced was whether Liverpool had actually missed a trick.
"Michael Edwards has been brought back to Anfield to take up a role which appears to be very similar to the one Klopp has now accepted. Would it have been possible to keep one of the club’s greatest-ever managers in the fold? Or did both sides agree that his time was up?
"If Klopp can impart his wisdom on to the Red Bull stable then it will prove to be a masterstroke of an appointment. But at the age of 57, I am sure he will eventually be desperate to get back out there on the grass at some point.
"If it’s accurate that Jurgen has a clause in his Red Bull contract that enables him to walk out should he be offered the chance to become coach of Germany, then it is obvious what his end-game is. And again, international football’s less demanding schedule will afford him that valuable time with his nearest and dearest."