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Coutinho, 28, is reportedly desperate to return to Anfield following a nightmare spell at Barcelona.
He has even made a personal plea to Klopp amid intense transfer speculation regarding his future.
Further reports claim the Brazilian midfielder is willing to take a pay cut to make the transfer happen in the summer.
Philippe Coutinho has made a personal plea to Jurgen Klopp in a bid to engineer his return to Anfield, according to @RealKevinPalmer- Anfield Watch (@AnfieldWatch) June 14, 2020
His agent has confirmed he wants to return to Liverpool, even if it means taking a pay cut to seal his return.
Would you take him back? pic.twitter.com/JhWcaEgxHy
Coutinho earns a believed £250,000-a-week at Barcelona. The La Liga giants are prepared to pay a portion of his wage if they send him out on loan again, but the Catalan club would prefer to sell him in a permanent deal.
The Barcelona man, who's currently on loan Bayern Munich, has also attracted interest from Manchester United, Leicester City and Newcastle United.
Klopp could be tempted to move in for Coutinho after failing to land RB Leipzig's Timo Werner, whose agreed to join Chelsea.
Former Liverpool defender Steve Nicol believes it's an "absolute no-brainer" for the Reds to resign Coutinho.
"Absolutely. Why wouldn't you? I can't think of one reason why you wouldn't," he explained.
"The only place he's excelled at is Liverpool. The place loves him, he loves the place. Can you imagine adding Coutinho to a squad that, right now are still champions of Europe even though they're out of this year's competition, and are going to win the Premier League?
"You're going to add a player with the ability of Coutinho, who is going to come in and be in the same situation as a Timo Werner for example, where he is there to fight to get in the starting XI.
"If it's cut-price, yeah. Listen, this guy's making over £13m clear a year. He's going to have to take a hit. The price to buy him is going to have to take a hit but if the money's right, [it's an] absolute no-brainer.
"If the money's right, this would be absolutely fantastic for Liverpool."
Coutinho to Liverpool? Watch this space.
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