"We are in the negotiation process and everything is on track," Laporta said at a Barca foundation event.
"We expect it to be resolved soon."
Talks with Valencia on Villa's transfer "are on the right track," Yuste said in an interview with Catalan radio station Ona FM quoted by Spanish news agency EFE.
Bringing Arsenal captain Fabregas back to Barca, where he was a youth player, was "more complicated because lengthy negotiations with his club lie ahead," Yuste added.
"But both players want to come and that makes everything easier," he said.
If the Gunners' skipper moved back to Barca, the 23-year-old, who has several years left on his Arsenal contract, would join international team mates Xavi and Andres Iniesta in the La Liga champions' midfield.
