Rijkaard tasted relegation before he was appointed. Not every manager has an infallible track record, neither should it be taken as a reflection of their true coaching abilities. Some thrive better under different(more familiar) environment and resources. This squad needs young blood, and Lucho has shown he's able to bring them up. Add, his Barca-affiliation as a player would be well embraced by the seniors. However, I don't think he'll assume the role unless he's guaranteed complete discretion in footballing matters.
The management seems keen on Valverde, having already approached him in the summer. If Martino steps down, I see them try again and bring him to the Camp Nou.