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.
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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.
The French champions paid a £34 million fee to Eintracht to secure his signature.
Liverpool have also been rejected by Real Sociedad midfielder Martin Zubimendi this week.