With Thiago supposedly looking to take on a new challenge after spending seven years at Bayern, Liverpool have been the club most strongly linked with a swoop for the 29-year-old.
However, Klopp already has a plethora of options in the middle of the park at Anfield, and according to Sky Sports News, Liverpool are not looking to sign any midfielders this summer.
The report claims that Thiago would jump at the chance to play under Klopp, and the Bayern man would be under consideration for a move to Liverpool should the Reds opt for change in the midfield.
Thiago only has one year left to run on his current deal with Bayern, where he has accumulated 31 goals from 232 appearances and lifted the Bundesliga title on seven occasions.
Paris Saint-Germain are also believed to be keeping a close eye on developments.