The midfielder was a surprise signing by Liverpool on loan from Juventus at the end of the summer transfer window.
He quickly picked up an injury and has been out of action, amid fierce criticism of Liverpool’s midfield this season.
It has been suggested that Arthur could return to Juventus early, but that is not the case and it is claimed there is zero chance of the Brazilian departing Anfield this month.
Arthur is ahead of schedule on his recovery from injury and is working hard to get himself back to full fitness.
He is expected to be available for Klopp to pick, if he chooses to, in the coming weeks.
Arthur is keen to get on the pitch at Liverpool and make an impact at Anfield before his loan comes to an end in the summer.
Liverpool do have an option to sign Arthur from Juventus on a permanent basis included in the loan agreement, but they have been tipped not to trigger it.
