The request was swiftly rejected by Liverpool, who released a statement insisting he is not for sale.
Liverpool sold Luis Suarez to Barcelona in 2014, after the Uruguay striker pushed for a move away from Anfield.
Philippe Coutinho has submitted a transfer request to Liverpool, according to reports from Sky.
Will Philippe Coutinho be announced as a Barcelona player anytime later next week or will we have to wait until the transfer deadline day to see the switch from Liverpool happening?
Klopp said: "I can't keep players happy - I can't keep you happy!"
Coutinho, 25, has spent the last four-and-a-half years at Liverpool, forging a reputation as one of the Premier League's top creative forces.
In a statement on Friday, the club's owners said its "definitive stance" was that "no offers will be considered".
When asked if he had to keep Coutinho happy, the German revealed the fact he is unavailable for selection due to a back injury is the greater problem. 'That is set in stone. "So what they pay in the end doesn't matter", Klopp told Sky Germany.
"Our goal is to have the best possible team".
Coutinho, who joined Liverpool from Inter Milan for £8.5m in 2013, signed a new five-year deal with the Merseyside outfit in January that did not include a buy-out clause.
The 28-capped Brazil worldwide has been suffering with a niggling back injury and it's unlikely that the Merseyside boss will want to risk the problem getting worse at the beginning of the season.
Coutinho was at his peak in the 2016/17 campaign, scoring 13 times and providing seven assists in 31 English Premier League appearances as Liverpool finished fourth and secured Champions League qualification.