Werner is now set to join Chelsea this summer after agreeing personal terms this week.
The Mirror says Klopp made clear to club bosses that he felt Werner would be a good fit at Anfield.
The Germany striker has grown and matured at RB Leipzig, into a prolific goal threat and top level marksman, boasting smart movement and rapid acceleration.
At 24, he has been clear that he wishes to take the next step in his career as he eyes further progression.
That was relayed in meetings and WhatsApp conversations between the pair, while the Kop boss outlined how he saw Werner fitting in on Merseyside, where Sadio Mane, Roberto Firmino and Mohamed Salah are already in place.
But with the Reds not interested in meeting his £52million release clause - which runs until June 15 - amid ongoing financial uncertainty due to the coronavirus crisis, and a new stand and training ground being paid for Klopp had to climb down and make clear to Werner that a switch wouldn't be happening this summer.