The 20-year-old made his international debut for Germany in the autumn and has impressed for Schalke in the Bundesliga.
Mundo Deportivo reports that Barcelona officials Robert Fernandez and Urbano Ortega flew to Germany to see the young midfielder in action against Mainz on Friday night.
Sane has a £28million release clause in his contract at Schalke.
Manchester City have previously been strongly linked with a move for the highly-rated midfielder.
