Arthur is undergoing an intense training programme at Liverpool in an attempt to ramp up his fitness, playing with the Under-21s and turning down the chance to take days off during the international break.
The Brazilian joined Liverpool from Juventus on an initial loan deal this summer, but has played just 15 minutes for his new side so far this season.
That's largely down to a lack of fitness, with the 26-year-old not playing at all for Juventus in pre-season.
He has admitted he's not in the shape he wants to be in, and has asked to be put on a particularly intensive training programme as a result.
"Arthur needs now just football, and training especially. That's how it is," said Jurgen Klopp recently.
"He wasn't in team training for a while at Juve, so he needs proper team training and that's what we are doing with him.
"Can he play minutes? Yes. Should he play a full game? No, because he needs to get used to the intensity in each competition. It's not like in the Champions League you have to work less than in the Premier League. Not at all, especially not here.
"He is doing well, he is really giving his absolute all in training, we have to be careful with him as well and then we will see whether we can use him."
The Daily Mail report that Arthur has requested to play matches with the U21 team, is doing double training sessions and has rejected the chance to take a few days off over the upcoming international break.
Liverpool return to action on October 1 against Brighton at Anfield.