The German confirmed earlier this month that he would be taking on the upstairs role with Red Bull from January onwards, a move that has triggered fierce criticism from both Liverpool and Borussia Dortmund supporters.
As part of his role, Klopp will be offering coaching support and identifying future talents for Red Bull's teams, including RB Leipzig, Red Bull Salzburg and New York Red Bulls.
The 57-year-old is already said to be drawing up transfer plans for his new job, as according to journalist Sebastien Vidal - via Sport - he has been alerted to the situations of two of Barcelona's La Masia talents.
The first of those is Aleix Garrido, a 20-year-old central midfielder who captains the Barca Atletic side and made his senior debut for the Blaugrana under Xavi in the 2022-23 La Liga season.
Klopp to poach two talents from Barcelona?
However, since coming off the bench for the final six minutes of that 4-0 win over Elche, Garrido has not made another appearance for the first team, although he was on the bench in the Champions League and La Liga last season.
Instead, the 2004-born talent continued his development with Barca Atletic in 2023-24, scoring one goal and setting up three more in 24 appearances, but he is yet to play a single minute this term due to a foot fracture.
Garrido - who has represented Spain at Under-19 level - could leave Barcelona on a free transfer at the end of the season, and Klopp is reportedly monitoring developments surrounding his contract.
The ex-Dortmund head coach is also said to be running the rule over 18-year-old attacker Noah Darvich, who joined Barcelona's youth system from Freiburg in a €2.5m (£2.1m) deal last year.
Unlike Garrido, Darvich - who can either play on the right wing or as a number 10 - has not made a senior appearance for La Blaugrana just yet, and he is without a goal or assist in six games for the youth team.
However, the 2006-born talent has enjoyed exceptional success with Germany, winning both the Under-17 World Cup and European Championship in 2023, making the team of the tournament in the latter event.
Darvich scored two goals and set up four more during Germany's run to continental glory last year, wearing the captain's armband in the process, and he now skippers the Under-19 Mannschaft side.
The teenager's Barca deal only runs for one more year than Garrido's, meaning that he could become a free agent in 2026, and an exit may be on the cards if he cannot break into the first team.
Which Red Bull teams could Klopp sign Barcelona duo for?
Klopp is apparently hoping to sign Garrido and Darvich for either RB Leipzig or Red Bull Salzburg, both of whom have been famed for their development of juvenile talents over the years.
The latter team are currently managed by Klopp's ex-Liverpool assistant Pep Lijnders and took two players from Anfield this summer, signing Bobby Clark permanently and Stefan Bajcetic on loan.