Roma want Liverpool to match their transfer record to land Mohamed Salah.
A £28 million bid for the Egypt international, 24, was rejected earlier this week by the Serie A runners-up, who had hoped to secure a £40m deal for the player.
But the Giallorossi are now hoping that the Reds will meet their lowered valuation of £35m, which would equal their highest current expenditure.
Andy Carroll became Anfield’s record signing when he moved from Newcastle United in January 2011 in a figure which has yet to be surpassed.
Liverpool’s approach has already received Salah’s backing, with the former Chelsea winger agreeing to terms of a £90,000 per week deal with the club.
But negotiations with Roma remain a firm sticking point, with the club currently in a state of redress to help comply with UEFA’s Financial Fair Play regulations.
Salah previously turned down a move to Liverpool in 2014 in favour of a mvoe to Chelesa, where his career stalled before spells with Fiorentina and Roma.