Kastrinakis says that the German boss told him as much during an "off-the-record" chat, in which he also admitted he "wants" to take over Liverpool and Real Madrid. Out of the three, United currently seems the most unlikely destination for Klopp.
Louis van Gaal has recently whipped the Red Devils into shape, and they are on course to qualify for next season's Champions League.
Currently sat third in the Premier League, United beat Tottenham Hotspur, Liverpool and Manchester City during a six-game winning streak in the league before losing to Chelsea on Saturday. They dictated the game at Stamford Bridge, even with a slew of late injuries to deal with, so things are heading in the right direction at the club.
Considering Van Gaal was only hired last summer, Klopp would likely need to wait until at least the end of the Dutchman's three-year contract before this move could be seriously considered. Both the Liverpool and Madrid jobs may be available at the end of the current campaign, however.
Brendan Rodgers' future is under the microscope after Liverpool lost Sunday's FA Cup semi-final to Aston Villa. Ian Ladyman of the Daily Mail labels Rodgers as a "flop," saying "he must take the blame" for the "failure" of this year's campaign.
Although the manager's inspired switch to 3-4-2-1 helped push Liverpool back into Champions League contention after an underwhelming start to the season, his team have developed a habit of falling short in the most important moments. John Percy of The Telegraph believes "the finger has to be pointed at Rodgers and his recruitment team."
Ian Hyland of the Daily Mirror joked about Rodgers' prospects:
Speculation over Carlo Ancelotti's future at Real Madrid also continues to make headlines. Sky Sports Spanish football expert Guillem Balague previously suggested Los Blancos' hierarchy are "seriously considering" axing the Italian.
The side are just two points behind Barcelona at La Liga's summit and remain in the Champions League.
Exiting European competition to neighbours Atletico Madrid—who head into the quarter-final second leg on the back of a 0-0 home draw—could provide president Florentino Perez with the excuse needed to dismiss his leading man. Klopp would be an exciting alternative.
At their best, Klopp's Dortmund play the kind of attacking football for which the aforementioned three teams are renowned. The German may need to bide his time if he's to land one of the most famous posts in the sport, however, particularly as all three are currently occupied.
Kastrinakis' publishing of the main points of his conversation with Klopp, if true, certainly makes for interesting reading. The man himself is yet to publicly acknowledge which nation and division he wishes to join next, and speculation about it will continue to swirl until he does.