Fekir enjoyed a superb campaign past year that saw him provide 23 goals and 8 assists to help Lyon finish third in the Ligue 1 table and his form saw him earn a place in the French squad that went on to lift the World Cup in Russian Federation last month.
Klopp also hinted that he will need to sell some of Liverpool's deadwood before the 5pm deadline on August 9.
Commenting on his relationship with them, Klopp said: "Absolutely, the relationship with the owners is strong".
It is claimed that a move to Chelsea could be cooled because of the fact Fekir would only be playing Europa League football next season.More news: Robert Mueller Seeks Interview with Russian Pop Singer Emin Agalarov
More news: Utility worker killed near Northern California wildfire
More news: Missing Iowa woman possibly sighted in Missouri
While the Reds do not hold any interest in the French global anymore, the player could still make his way to the Premier League, with Chelsea setting their sights on him.
"I can not kill your D-day [Sky Sports Deadline Day] show, people sit there in front of the television all day waiting". When Manchester United visit Anfield in December, I'm sure they'll use every trick in the book to try to wind him up! "I feel brilliant in this squad".
"He's quite a good footballer - probably as good as the goalie he is", Klopp told reporters after the match. France Football are reporting that Fekir could complete a move to Stamford Bridge by Thursday when the transfer window closes. "He probably won't play Tuesday and Sunday will be very hard as well", continued the German, who is known to stick to a very rigorous training strategy.
"We live well and I hope that OL will have a great season".
Fekir, who is under contract with Lyon until 2020, scored or assisted 31 goals for the French outlet last season.