Arthur will not return to Juventus in January and could stay at Liverpool beyond this season, the midfielder's agent said.
Brazil international Arthur has played just 13 minutes for Liverpool since joining on loan from Juventus in September, being sidelined by a muscle injury that required surgery.
The 26-year-old is expected to return to action before the end of December, but recent reports suggested he may head back to his parent club next month.
However, agent Federico Pastorello has denied those claims and suggested there is a chance of Arthur staying at Anfield for the long term should his Juve future not be resolved.
"He will stay at Liverpool in January, 100 per cent," Pastorello told Tuttomercatoweb. "It's an aspect that has never been under discussion.
"I don't know who has started these rumours regarding a return to Turin, but that is not the case, absolutely. It is not foreseen in the contract and there is no possibility.
"Nobody has questioned his stay – not Liverpool nor Juventus. As far as next season is concerned, when the current one ends we'll see.
"If [Massimiliano] Allegri continues at Juve, a solution will have to be found. If Liverpool want to renew the loan or make an offer, I think they'll find fertile ground."
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Liverpool have the right to buy Arthur, who previously spent two years with Barcelona prior to joining Juventus in June 2020. The option entails a reported £32.3million (€37.5m) fee to be paid at the end of the season.
The Gremio academy product was a surprise signing for Liverpool on deadline day in the past transfer window, and Pastorello has revealed how the move came about.
"The operation was born out of stubbornness to look for something," Pastorello said. "Liverpool had previously given signs of approval, but they didn't have space [in the squad]."
He said Liverpool made an approach when Jordan Henderson suffered an injury.
"It was the penultimate day of the transfer market. Liverpool called us saying they wanted to close the deal and from there we got down to business," the agent added. "We left for Liverpool on the last transfer day for visits and signings."
Arthur is one of 12 midfielders to have featured for Liverpool this season, yet they continue to be linked with the likes of Sofyan Amrabat, Enzo Fernandez and Jude Bellingham.
Jurgen Klopp's side return to competitive action on Thursday following the World Cup break with a trip to Manchester City in the last 16 of the EFL Cup.