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Laporta wants the long-delayed project to start next summer and although he expects work to last three to four years, he believes the team will need to move out for a maximum of 12 months.
"We are considering different possibilities, but the strongest candidate is the Johan Cruyff Stadium," Laporta told Catalan radio Rac1.
Johan Cruyff Stadium is where the women's team play and forms part of the club's training complex on the outskirts of Barcelona.
With a capacity to seat only 6,000 spectators, Laporta said the club want to increase that to 50,000 if the men's team move there.
Another option, Laporta said, would be for the team to play at the city's Montjuic Stadium. The municipal facility hosted the opening ceremonies of the 1992 Summer Olympics and was home to Barcelona rival Espanyol for several years.
The Nou Camp is already Europe's largest football stadium with 99,000 seats. The club want to increase its capacity to 110,000 while also refurbishing its surrounding area, which includes a pavilion for the club's other sports, the museum and stores.
Barcelona are in talks with Goldman Sachs for the investment bank to loan the cash-strapped club £1.25billion but that financing plan needs to win a vote by the club's members.
Laporta inherited a club near bankruptcy when he won elections in March. He had also led the club from 2003-10.
"(The new Nou Camp) is fundamental for the viability of the club and its immediate future," Laporta said. "The impact it will have for Barca is critical so that we can compete with our competitors who have already done what is needed."