The signs look great for Liverpool ahead of next weekend's Premier League kick-off, with Brazil goalkeeper Alisson keeping a clean sheet on his debut in the 5-0 demolition of Carlo Ancelotti's side in Dublin.
Liverpool had hoped to announce the 25-year-old before the World Cup began and the deal was so advanced, he had agreed personal terms on a five-year contract and also conducted an introductory interview with LFCTV, the club's in-house television channel.
Blues boss Maurizio Sarri has recently indicated that the club may pursue one recruit before the transfer deadline and Fekir could preferably be the choice before the transfer window closes on Thursday.
Persistent rumours have suggested Liverpool may try to revive the deal, but those stories have been emanating from France rather than Merseyside and Anfield insiders have suggested they have not re-opened talks with Lyon over a fresh deal for Fekir.
"I can imagine you want to hear about that, he's an outstanding talent, outstanding", Klopp told Liverpool's official website after the game at the Aviva Stadium.
"I am a very positive person but even I can not say that reaching a final is the maximum because it's not the maximum".
Liverpool next play Torino on Tuesday night, but it is unlikely that Alisson will feature again as Loris Karius is primed to get the nod in the Reds' final pre-season fixture of the summer.
"I don't know in the moment how many really good goalkeepers Ireland has, but having one more is never a big mistake".
"What I like that Klopp has done is he has signed quality where he has needed it - the middle of the park they were lacking - there is great competition for places and he did it early".
"Hopefully it will be good and that's very important".