The Catalan is keen to see the No.10 stay on at the Camp Nou for the 2021/22 season, despite his contract having expired at the end of June.
"We're waiting for him to sign the renewal and to have him with us," Pique said.
"I hope he's convinced."
Barcelona had a disastrous start to the 2020/21 season, which ultimately proved to be their downfall as they mounted an unlikely comeback in the title race, only to fall short in the final weeks of the season.
With LaLiga Santander being described as the "foundation for the rest of the season", Pique is hungry for a strong start domestically.
"I'm going into this season with the same enthusiasm as my first," Pique said.
"We must try to start well. Generally, when we win league titles, it's because we pick up a good rhythm from the start and pull clear, or we build up a lead and maintain it.
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