Dr. Jean-Louis Bonnet, chief of the cardiology unit at La Timone hospital in Marseille, says "everything's going well" and that Jarreau's "state of health is coming along quite normally."
Bonnet said Tuesday the singer could possibly be discharged over the weekend and could then continue his scheduled European concert tour.
The 70-year-old Jarreau was hospitalized in the Alps on Friday after suffering breathing problems in the mountains that forced him to cancel several concerts. He was moved to Marseille by helicopter Saturday.
Jarreau has won Grammys in three separate categories - jazz, pop and R&B.