Prodigious Dutchman de Ligt emerged as one of Europe's elite centre-backs last season with Ajax at the tender age of 19.
Barcelona were the early favourites to purchase him, having already secured the services of his close friend and fellow youn Ajax star Frenkie de Jong, before the defender eventually chose Italian giants Juve.
Grau discussed missed transfer targets at the presentation of Barcelona's budget, implying de Ligt turned down their offer purely for financial reasons.
“We made him an offer, but he preferred to go to Juve, where Italian taxation allows him to earn a higher net salary.” said Grau.
The Catalan club also made "a very big effort" to bring back Brazilian superstar Neymar, he added.
“The club did everything possible with two offers, one with and one without players in exchange, but still sustainable.
“The feeling, though, is that PSG never really opened up to a sale.”