The Spanish giants are searching for a replacement for Luis Enrique, who announced at the start of March he would leave at season's end.
Barca are expected to announce their new coach on Monday and Valverde, heavily linked with the position, has stepped down as Athletic Bilbao boss.
Pique would welcome the arrival of the 53-year-old, who played for Barca from 1988-1990.
"Ernesto has done a great job at Athletic the last few years," he said.
"He played here for Barcelona as a player and I think he could be a good option, as could others.
"I can't decide myself on anyone and I don't know who will be the next manager. It's not my job and I haven't put a lot of thought into it."
He then led Olympiakos to three league titles and two cups, and helped Bilbao win the 2015 Supercopa de Espana against Barca.