Cancelo and Felix spent last season with the Catalan giants on loan from Manchester City and Atletico Madrid respectively, and the pair were regulars for the club in 2023-24.
As it stands, both players will head back to their parent clubs after representing Portugal at this summer's European Championship.
However, Laporta has revealed that Barcelona are working to keep hold of them for the 2024-25 season, with further loan deals potentially being agreed due to the club's financial issues.
"We want them to continue. Deco is working to ensure that they continue another season in the current conditions," Laporta said on the President's Podcast on Barca One.
Barcelona want to keep Cancelo, Felix at Camp Nou
"[Hansi] Flick considers that they are high-quality players and when he coached Bayern he already tried to incorporate Joao Felix. I think that Felix could have performed better because he has extraordinary quality."
Cancelo scored four goals and registered five assists in 42 appearances for Barcelona during the 2023-24 campaign, including two goals and four assists in 32 league matches.
Felix, meanwhile, featured on 44 occasions for the Catalan team last term, scoring 10 goals and registering six assists in the process.
The 24-year-old netted seven times and registered three assists in 30 La Liga appearances, while he also scored three times and provided one assist in nine Champions League outings.
Laporta has also confirmed that his club could look to bring in a new holding midfielder during this summer's transfer window.
Barcelona could bring in a central midfielder this summer
"We are studying the positions to be reinforced with Flick. In the pivot, with [Andreas] Christensen, the team took on another dimension, but it is a position in which another player may need to join," he revealed.
"In the quarry, we have Marc Casado, who has had an extraordinary season. We're not talking about players, we're talking about positions."
Barcelona finished second behind Real Madrid in La Liga during the 2023-24 campaign, while they made it to the quarter-finals of both the Champions League and Copa del Rey.
Flick was appointed head coach of the Catalan giants at the end of last month following Xavi's surprise departure, with the ex-Bayern Munich and Germany manager arriving on a two-year contract.
Sergi Roberto is one of two Barcelona players out of contract this summer, but Laporta also confirmed that hie club are planning to keep hold of the Spaniard, with a 12-month extension in his contract likely to be activated.