Klopp is on a sabbatical at the moment, but the German is reportedly open to cutting short his break.
However, according to Sky Sports, the 48-year-old, who has been without a managerial job since the end of the 2014-15 season, has not been contacted by Liverpool yet.
Former Liverpool striker Fowler has taken to Twitter to give his reaction to the reports that Klopp is interested in becoming the new Liverpool boss (although he has not mentioned the German by name).
Top story on @SkySports Just a little tip for you 99% of managers are interested in working in prem and all would cut short sabbatical— Robbie Fowler (@Robbie9Fowler) September 24, 2015
Brendan Rodgers has been in charge of Liverpool since the summer of 2012, but he has come under pressure this campaign.
The Reds are 13th in the Premier League table at the moment with eight points from six matches, four points behind fourth-place Leicester City.