Rashford, a 27-year-old England international, joined Barcelona on a temporary loan deal with an option to buy from his boyhood club, Manchester United, earlier in the summer.
However, due to the club's ongoing financial difficulties, they have yet to register Rashford for the upcoming La Liga season.
In an interview with a local sports publication, Laporta stated that, in principle, there will be no further signings.
Laporta explained that the club's coach wants to make adjustments to the first team's dynamics using players from Barcelona Atletic, the reserve team.
He emphasized that the club will aim to avoid releasing any players, but acknowledged that some adjustments will be necessary to address the issue of too many players in certain positions.
Laporta stated that the coach and Deco, a former player and current member of the club's board, will have the final say in deciding which players to release.