Guardiola, 40, hinted he may leave the club in an interview with Italian television channel Rai this month, saying: "I think my time is ending here in Barcelona."
"Next year will be my fourth consecutive as Barca coach. A club like this must have a lot of courage to keep a coach for all this time because players tire of coaches and vice versa," he added.
But in an interview published on Monday in daily newspaper El Mundo, Alves said he and the rest of the squad want him to stay on.
"We follow him with our eyes shut. He is very intelligent, he always knows what he is doing. To not follow Guardiola would be foolish. Since we are not foolish we will follow him until he gets tired of us," he said.
"Everyone has their cycle and one day his will come to an end. We hope his cycle will last for a very long time because we can't imagine Barca without Guardiola," the 27-year-old Brazilian international added.
Guardiola, who spent most of his playing career at Barcelona, coached Barcelona's B team before taking control of the first-team squad in June 2008 from Dutchman Frank Rijkaard.
The former Spanish international midfielder has won eight trophies, including successive La Liga titles and the 2009 Champions League, since taking over Barcelona's senior team.
Barcelona held Real Madrid to a 1-1 draw on Saturday, leaving them eight points ahead and well placed to clinch their second straight league title.
The two sides will meet again on Wednesday in the King's Cup final at Valencia's Mestalla stadium, with Real coach Jose Mourinho aiming to win his first trophy with the club.
Barcelona and Real will also face off twice in the Champions League semi-finals, with the first leg at the Bernabeu on April 27 and the return leg on May 3 at Camp Nou.