The 23-year-old left the squad, who are in the Far East to play in the Premier League Asia Trophy, to finalise the details of a move which, Press Association Sport understands, could eventually cost the Tigers up to £8million.
However, it is understood the move is not tied in with a deal for the Sky Bet Championship side's left-back Andrew Robertson to go in the opposite direction and Liverpool will pursue that separately.
Stewart, who signed a new four-year contract in February last year, played only nine times last season, including just four league appearances, and would have struggled to get a place in the match-day squad this season barring a number of injuries to other players.
Even the departure of established first-team midfielder Lucas Leiva to Lazio on Tuesday did not improve his chances
Stewart joined Liverpool in 2014 after being released by Tottenham.
Source : PA
Source: PA