The 25-year-old, the club's highest-paid player after signing a new five-year, Â£150,000-a-week contract in January, tried to force an exit by asking to leave after Barcelona had a third bid of £90million up front rejected.
Owners Fenway Sports Group issued a statement insisting Coutinho would remain a Liverpool player when the summer window closed and that has proved to be the case, although since then there have been reports suggesting he does not want to play for the club again.
The player was unavailable for the Reds' first five matches with an apparent back injury but came off the bench to score for Brazil in a World Cup qualifier against Ecuador on Thursday and is expected to feature against Colombia on Tuesday before returning to Melwood.
It remains to be seen whether he will be considered for Saturday's trip to top-four rivals Manchester City but Klopp is happy to still have the player available to him.
"We still have a really good player in the squad who can play," said Klopp, speaking to German media outlet SPORT1 after coaching in Nikolce Noveski's testimonial game at former club Mainz.
"Don't believe everything in the press or that there are offers here and there and that the minute after the offer has been entered, it should already be over.
"We are not like George Orwell where everybody knows everything immediately. We have exactly the situation we wanted and no other."