According to the player's father Jesus Lozano, the World Cup star will decide whether to speak with Barca when he returns from Russia.
"There's been an approach from Barça but there's nothing clear at the moment. When the World Cup's over, we will have a better idea of the reality: if he will stay at PSV or move to another team," he told ESPN.
Lozano made the headlines at the World Cup when he scored the only goal in Mexico's shock 1-0 victory over Germany.
English clubs including Everton have also been linked with the PSV forward.