The 21-year-old currently has four goals and one assist this season after finding the back of the net 16 times in the 2020-21 campaign, while also setting up eight.
With Liverpool currently relying on Roberto Firmino and Diogo Jota as their lead strikers, it is understood that Klopp would like to bring in another forward, with Gouiri fitting the bill.
According to Fichajes, the German has requested that the club make a bid to try and sign the Ligue 1 striker, as he is currently top of his wishlist.
Klopp is said to be an admirer of Gouriri's performances, while his two forwards currently have one goal each in the Premier League so far this season.
Liverpool are without Firmino at the moment as he is dealing with a hamstring injury that saw him hobble off during their game with Chelsea.