Announcing his departure, Hull said: "The 23-year-old full-back left the Tigers' Portuguese training camp earlier this week to undergo a medical and finalise terms with the Merseyside club".
The Brazilian struggled to hold down a regular spot under Klopp, and was often deployed in defence, but the German had nothing but praise for the Rome-bound player.
Naby Keita of RB Leipzig is challenged by Almog Cohen and Stefan Lex of FC Ingolstadt 04 during the Bundesliga match between RB Leipzig and FC Ingolstadt 04 at Red Bull Arena on April 29, 2017 in Leipzig, Germany.
One of the major drama this summer has been the transfer saga of Naby Keita to Liverpool. I had to say: "'If you don't want to be involved because you don't feel OK then you have to train alone until this period of time is over". The club told me they will not sell Virgil.
Liverpool fans, are you excited about this potential news? Such a valuation for a relatively unproven player has been described as "insane", although Liverpool's latest offer was close to that figure.
Having flown to Portugal for his medical, Stewart could make his first Hull appearance in Saturday's friendly against Benfica.
"I repeat that the club said no [to a sale]".
"What can I say?" Either that, or he should remember that selling players in the transfer market requires the agreement of two clubs, not just his own. "He will stay patient, 100 per cent and we will help him all we can, and then hopefully, in the end, everything will be good".
Leipzig remain unwilling to deviate from their stance that no players are sellable, with founder and owner Dietrich Mateschitz insisting that money is not an issue.