Liverpool attempted a last-minute hijack to sign new PSG addition Willian Pacho this summer.
The Reds did put in a higher offer than the French club when he was leaving Eintracht Frankfurt.
However, Le 10 Sport states that the defender turned down the move to Anfield.
He is said to have preferred going to the Paris-based team, where he now plays.
Liverpool have also been rejected by Real Sociedad midfielder Martin Zubimendi this week.
