The 19-year-old has been identified as a priority target by the club's new head coach Andoni Iraola, who replaced Arne Slot in the Anfield dugout this summer.
Ornstein reported that Liverpool had informed Leipzig they were willing to pay a package worth €100m for the Ivory Coast international, who impressed in the Bundesliga last season and in Ivory Coast's World Cup opener against Ecuador.
Romano added that Leipzig turned the approach down, with the German club holding out for a fee in excess of that figure, with €120m mooted as a possible benchmark.
Liverpool have already moved to address the width of their attack, spending £34.5m on Osasuna forward Victor Munoz, who was confirmed as a Reds player this week, hijacking a move that had been progressing at Newcastle United.
Diomande would add a different dimension to the overhaul, with the teenager having come through RB Leipzig's academy system before making his first-team breakthrough last season.
RB Leipzig signed Diomande from Ivory Coast club Stade d'Abidjan for a relatively modest fee and he developed quickly through their system, with his combination of pace, pressing intensity and technical ability making him one of the standout young forwards in the Bundesliga last season.
Whether Liverpool return with an improved offer or shift focus to alternative targets remains to be seen, but the club's need to reinforce their wide areas after a summer of significant departures makes another approach likely.