Messi, 33, is out of contract in June and is free to negotiate a pre-contract agreement with any club from January onwards.
The forward wanted to leave Camp Nou after August's 8-2 defeat to Bayern Munich in the Champions League, with sources telling ESPN that Manchester City led the race to sign him, but he was eventually forced to stay put.
"You will have to ask Leo, I don't know," Pique said in a question and answer session for the CRIS Cancer Foundation when asked if Messi would remain at Barca beyond the summer.
"We hope he stays. It's a personal decision. We will see. But for as long as he's wearing the Barca shirt, there is always hope. We hope to seduce him to stay for many more years."
Barca have been unable to start talks over a new deal with Messi because they have been left without a president since Josep Maria Bartomeu resigned in October.
A new president will be elected at the end of January, with Victor Font and Joan Laporta among the early favourites. Only then will the club be able to try and convince Messi to sign a contract extension.
"Messi had a good break this week, as did Frenkie de Jong," Barca coach Ronald Koeman said in a news conference on Saturday.
"Both had played nearly every minute for us this season, in addition to many games with their national teams.
"They can't keep going and going and going. To avoid problems, we left them at home in midweek. But we will need them [against Osasuna]."
Midfielder Sergio Busquets is also back in contention after missing the last two games with a knee problem, although Pique, Ronald Araujo, Samuel Umtiti, Sergi Roberto and Ansu Fati are all missing with injuries.
United States international Sergino Dest is also a doubt, with a decision on his fitness to be made on the morning of the game.
"It isn't serious because Dest trained [on Saturday] but he came back really tired back after the match against Kiev and he had some [muscle] problems," Koeman said.
"We will not take any big risks with him because in his position we have a lot of players injured. If he's OK, he will start; if we have doubts, he will not start."
Barca have made their worst start to a league season since 1991 and sit 13th in the table with 11 points from eight matches.
However, Koeman believes their luck is about to change with a favourable run of fixtures between now and the end of the year.
"We have seven league games coming up and five of them are at home," he added. "The time to react is now. We have to cut the gap on those at the top of the league."