The Spanish champions are said to like his versatility, his work ethic and ability to provide assists for team-mates (he finished the season with eight goals and six assists in La Liga).
The striker may not come cheap though. His current deal runs for another three years, and he has a release clause of €120 million. There is also reported interest from Roma.
Sport reckon that Rodrigo goes quite fancy the idea of moving to Barcelona as it would help boost his international hopes.
However, the Valencia man is also a little wary about playing time, particularly having seen Paco Alcacer swap Valencia for Barcelona and barely feature before heading off to Borussia Dortmund.