The Paraguayan international striker made a good start to life in the Premier League last season as he scored 23 goals for Rovers in his first season in England.
However, despite the fact that he still has three years remaining on his contract at Ewood Park, Santa Cruz told La Nacion that United are interested in taking him to Old Trafford.
"The interest from Manchester United is real but I'm busy now so my representatives will handle anything if there is a concrete offer," said the 26-year-old forward.