According to multiple outlets including The Telegraph, the 23-year-old midfielder has been given permission to fly back to the United Kingdom from Hong Kong, where Jurgen Klopp's side are due to open their Premier League Asia Trophy campaign against Crystal Palace later on Wednesday afternoon (19 July), in order to wrap up an £8m ($10.4m) permanent transfer.
The deal is said to be separate from Liverpool's pursuit of Hull left-back Andrew Robertson, for whom they are said to have agreed a £10m fee as they edge closer to their third signing of the summer transfer window thus far.
Lucas, formerly the club's longest-serving player, joined Serie A outfit Lazio yesterday in a deal believed to be worth £5m.
Stewart moved to Anfield three years ago following his release by Tottenham Hotspur and was subsequently sent out on loan to Cheltenham Town, Burton Albion and Swindon Town before being recalled by Klopp last January in order to make his senior debut in an FA Cup tie against Exeter City. He featured a further 19 times across all competitions and was only handed a new four-year contract in February 2016.
The 23-year-old is primed to become Hull boss Leonid Slutsky's third signing at the KCOM Stadium, following Chelsea defender Ola Aina and free agent striker Frazier Campbell.
Aside from Stewart and Lucas, the only other senior players to depart Liverpool so far this summer are veteran goalkeeper Alex Manninger and academy graduate right-back Andre Wisdom. The former retired following the end of his one-year deal, while the latter joined Derby County for a fee of around £3m. Youngsters Adam Phillips, Tom Brewitt, Jack Dunn, Madger Gomes, Kane Lewis and Jake Brimmer were all released.
Liverpool are without Sadio Mane in the Far East, with the influential forward set to return to full training next week. The club further confirmed on Wednesday that right-back Nathaniel Clyne, who did travel to Hong Kong, would also miss the Asia Trophy due to a lingering muscle strain.
The England international is expected to rejoin training when the squad head to Germany later this month for a match against Hertha Berlin and the Audi Cup tournament in Munich. However, Alberto Moreno, whose uncertain position under Klopp looks set to become even more precarious by the arrival of Robertson, is now fit again.