The Reds were not initially expected to dip into their war chest for a new midfielder in the summer window, but injuries to a number of key players forced Jurgen Klopp's hand.
Thiago Alcantara, Curtis Jones, Naby Keita, Jordan Henderson and Alex Oxlade-Chamberlain have all spent time on the sidelines, which led Klopp to sanction a deadline-day loan move for Arthur from Juventus.
The former Barcelona man is still working his way towards full match fitness, though, and he is yet to start a game for the senior Liverpool team in any competition.
According to The Times, in a bid to kickstart his career at Anfield, Arthur has enlisted the services of nutritionist Joana Pessoa Dell'Oro, physiotherapist Adrian Martinez Castro and fitness coach Daniel Esteban Labarca Encina to work in tandem with him.
Arthur made his debut for Liverpool in their 4-1 Champions League defeat to Napoli earlier this month, coming off the bench for the final 13 minutes after James Milner was selected ahead of him.
The Brazil international then failed to earn any minutes against Ajax and was previously an unused substitute in the Merseyside derby with Everton after his work permit was sorted quicker than expected.
In order to ramp up his preparations for first-team action, Arthur has taken to life with the Under-21s squad and played the full 90 minutes in a 1-0 Premier League 2 win over Leicester City on September 17.
The 26-year-old was then selected for EFL Trophy action against Rochdale, and he lasted an hour of that 1-0 defeat before being taken off for returning player-coach Jay Spearing.
Liverpool played just the one Premier League game in September due to the death and state funeral of Queen Elizabeth II, which saw Arthur drop down to the youth levels for fitness reasons.
Barry Lewtas was quick to hail Arthur's "professionalism" after he arrived for Under-21s action, telling the Liverpool Echo: "Arthur has been in over the international break to play games and build up his fitness.
'That's off his own back, so that shows his level of professionalism. He has been great with the lads as well. He has been first-class."
There had been suggestions that Liverpool could have terminated Arthur's loan deal in January if they were able to sign a new midfielder, but the Brazilian is expected to see out his loan deal.
An option to make Arthur's stay permanent for a fee of €37.5m (£33.1m) has been included in the deal, but Liverpool are unlikely to activate it as they prioritise a summer move for Borussia Dortmund's Jude Bellingham,
Arthur will endeavour to make his Premier League debut for Liverpool when they take on Brighton & Hove Albion at Anfield on October 1 following the international break.