Lozano, known as 'Chucky', rocked world champions Germany in Mexico's opening match at the 2018 World Cup, scoring the winning goal in his side's stunning 1-0 victory.
The 22-year-old enjoyed a breakout season at PSV Eindhoven in 2017-18, scoring 19 goals and providing 11 assists in 34 appearances in all competitions, and his World Cup debut appears to have gained him even more admirers.
Indeed, Jesus Lozano has confirmed that the Catalan giants are interested in his son's services, but he is unsure if a move will be sanctioned this summer.
"There's been an approach from Barça but there's nothing clear at the moment," Lozano Sr. told ESPN Mexico.
"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."
"I just think that whoever takes a chance on him will do well. His pace and again his ability to take people on, he can play in any league and any place," he told Sky Sports News.
"I think he will be able to - and he has the tools to play - in the Premier League."