Pique wants Valverde to continue as Barca boss
It had been believed that Valverde's contract was due to expire at the end of the current campaign, though Barca president Josep Maria Bartomeu revealed in October that the 54-year-old's deal runs until 2020.
However, Valverde and Barca have the option to terminate the contract a year early.
Speaking after Barcelona's 2-1 victory at Getafe on Sunday, centre-back Pique said: "It's a decision that he will make and we will respect because he is the coach.
"We would be delighted if he decided to continue and he is doing a magnificent job.
"He brings calmness and he is producing results and showing that his way works."
3 points, for 3 Kings. The perfect Reyes Magos present. pic.twitter.com/3cUHptNBCs— FC Barcelona (@FCBarcelona) January 6, 2019
Lionel Messi and Luis Suarez scored as reigning champions Barcelona moved five points clear atop the table after 18 rounds.
Barca are now 10 points ahead of fifth-placed Real Madrid, who were stunned 2-0 by Real Sociedad.
"I don't know if it's a major blow to LaLiga, in terms of the points between us and the rivals," Pique said.
"It's always good to come back from the Christmas break with a win. I think it's years since we did it."