Earlier this week it was reported in Spanish newspapers that Moreno had told his Sevilla teammates he would be joining Real Madrid at the end of the season.
United transfer target Fabio Coentrao is expected to leave the club this summer, and Carlo Ancelotti wants to bring in fresh competition for first-choice left-back Marcelo.
Moreno, 21, has been one of the standout young stars in La Liga this season, impressing for Sevilla and even earning his first full caps for the Spanish national team.
But the Daily Mirror claims Liverpool retain hope of convincing Moreno to join the Anfield club. They hope to capitalise on Madrid’s propensity to target big-name, big-money players early in the window.
Liverpool boss Brendan Rodgers is prepared to pay up to £15m to land the full-back, with left-back a real area of need for the Reds manager.
On-loan defender Aly Cissokho will be allowed to return to Valencia at the end of the season after failing to earn a permanent deal.
But Liverpool could still face competition from Manchester United, who are waiting to see what happens with first-choice full-back Patrice Evra. The Frenchman is out of contract at Old Trafford this summer.