Jurgen Klopp's side have yet to agree a new deal for Dutchman Georginio Wijnaldum, whose future at Anfield has been shrouded in doubt since the summer, and he has been heavily linked with a move to Barcelona.
Liverpool's latest offer is believed to have 'fallen short of the mark', although the Anfield club are expected to revise their bid in the hope of finalising a deal soon.
The price tag on De Paul is rumoured to be around £31m and that could well be signed off by Reds sporting director Michael Edwards.
De Paul, who has 21 senior caps for the Argentine national team, has scored three time and provided three assists for Udinese in Serie A this campaign. body check tags ::