Speculation over Rooney's future at Old Trafford has been brewing for months, with David Moyes thought to be undecided over the forward's long-term future ahead of talks this week.
Despite rumoured interest from a string of European clubs including Real Madrid, Arsenal and Chelsea the Catalan giants are prepared to enter the race for his signature, according to The Sun.
"Rooney is precisely the type of attacker that would fit perfectly into the system," the newspaper quotes a source at Barca as saying.
"Defence starts from the front at Barca and Rooney works harder than anyone. His first touch, movement, control and vision are phenomenal and if he comes on the market then the club are certain to try to sign him."
Despite signing Neymar in the close season Barca boss Tito Vilanova reportedly still wants a replacement for David Villa this summer, with Rooney thought to be available for around £25m.