"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."
Club vice-president Rafael Yuste had earlier claimed that Barcelona were in talks with Villa and Arsenal midfielder Cesc Fabregas.
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.
An Arsenal spokesperson said the Premier League club never commented on transfer speculation with a Valencia spokeswoman adding that the La Liga club had no immediate comment.
Fabregas is currently recovering from a cracked bone in his right leg and should be fit to help European champions Spain in their bid for a first World Cup triumph in South Africa starting next month.
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.
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