Elliott made his request directly to his manager and negotiations between the two clubs are understood to be at an advanced stage, with a straightforward loan the preferred structure for the deal.
The 23-year-old has agreed personal terms with Valencia, according to reports in Spain, and the move is expected to be finalised before Tuesday's transfer deadline.
The England youth international has found himself on the fringes at Anfield this season, left out of Liverpool's matchday squad for the club's Premier League opener against Newcastle United as Iraola opted for youngsters Lewis Koumas and James McConnell instead.
Speaking before Liverpool's fixture against Nottingham Forest, Iraola said finding a place for Elliott had come down to "finding the balance on the bench," adding: "In Harvey's case, he's trying, he's improving every week, but I still prefer other options."
Elliott's stock has fallen since a difficult season-long loan at Aston Villa in 2025-26, a move that was reportedly structured so that Villa avoided triggering a £35m obligation to buy by limiting him to just four appearances.
He returned to Liverpool this summer and impressed during pre-season, including with an assist against Sunderland, but has remained behind the likes of Florian Wirtz and Dominik Szoboszlai in the pecking order. Napoli and Lazio had also shown interest in the midfielder, but Valencia are understood to have won the race for his signature.
A move to Mestalla would give Elliott, who has one year left on his Liverpool contract, the chance to rebuild his career with regular first-team football, something increasingly hard to find at Anfield following the club's pursuit of Bradley Barcola this week.
Elliott joined Liverpool's academy from Fulham in 2019 and has gone on to make well over 150 appearances for the club, winning the Premier League and League Cup among his honours, but he has struggled to establish himself as a guaranteed starter since Liverpool's summer investment in midfield and attacking options under the new regime.