The German club has rejected Liverpool's record-breaking bid of £100m upfront plus £13m in bonuses for Wirtz.
Instead, Bayer Leverkusen are insisting on a higher price of £126m for the 20-year-old Germany international.
Liverpool's chief, Richard Hughes, is eager to sign Wirtz before the Club World Cup transfer window closes on Tuesday.
It is unclear at this time whether Liverpool will meet Bayer Leverkusen's demands or look for an alternative player.
