Josep Maria Bartomeu's recent resignation has left a hole in the hierarchy of the club, and the election process to appoint his successor has been scheduled for January.
However, 33-year-old central defender Pique ruled himself out of contention for the current vacancy, telling Marca: "In the elections that come now, I'm not able to run because I am still a player and when you're a player you can't run for the position, but you never know in the future.
"I am very, very, very [connected to Barcelona] as you know. I would like to be able to help the club of my heart in the best way I know how, and that happens because I am very well-prepared to serve as president if one day I see that I can really contribute to the club. If not, I would not show up.
"It is something that I will decide in the future, it is a dream of mine that I have always had, but I do not know if it can be carried out in the future."
Pique signed a new contract in October that runs until the end of the 2023-24 season, at which point he may revisit his ambition of taking the top job at Barcelona.