It is just over two weeks since the shock move to bring in Brazilian midfielder Arthur on a season-long loan from Juventus.
The decision to sanction a temporary deal came in the wake of Jordan Hendersons hamstring injury, which added to issues for Naby Keita, Alex Oxlade-Chamberlain and Curtis Jones.
In fact, so far this season, Fabinho, Harvey Elliott and James Milner are the only midfielders not to have missed a game through injury.
Arthur was not brought in to fill a first-choice role in Klopps side, but earlier this week, claims from Italian outlet TuttoMercatoWeb suggested his stay could even get cut short.
It was argued that he is not at the level that was expected, with his 13-minute cameo against Napoli said to be enough to understand that he does not fit the type of player that Jurgen Klopp was looking for.
They claimed that Liverpool would not be afraid to terminate Arthurs loan agreement in January, particularly if they bring in another midfielder.
Of course, the source is far from reliable, though speculation was picked up by the likes of the Liverpool Echo and SportBible.
But journalist Guillem Balague, who seems to hold connections to Arthur having been among those to break the news on his switch to Merseyside, has moved to dismiss rumours.
Liverpool have not decided to extend the loan or buy Arthur but have no intention to send him back in January. They are still assessing him, Balague wrote on Twitter.
In fact, the coaching staff congratulated him on his understanding of the system and his quality.
He decided to ignore days off to keep working as he knows he still has got to catch up with demands.
Hes working on an individualised fitness plan to get him up to speed because he didnt have a regular pre-season. Pretty standard stuff considering the lack of match fitness.
As Balague notes, it is no surprise that Liverpool are taking a cautious approach to Arthurs fitness, with the 26-year-old having only clocked 1,533 minutes for Juventus last term and not featured during their pre-season.
With Thiago now back fit and both Henderson and Jones not expected to be far off, the competition for places in Klopps midfield will only increase.
However, it seems there is no chance at this stage that the Arthur deal will be cut short.