Villa, Spain's all-time leading scorer who joined Barca from Valencia two years ago, fractured his left leg at the Club World Cup and has not played since.
The 30-year-old missed Spain's triumphant Euro 2012 campaign but has already returned to training with his club team-mates for the start of La Liga on the weekend of Aug. 18-19.
"David Villa is no longer in the hands of the doctors, he is now in the hands of the rehabilitators," Cugat said on Barca's website.
"He seems in good shape, full of desire, hope and intensity," Puyol said.
"What happens is that with such a long-term injury the most important thing is not to rush," he added.
"I spoke to him the other day and the issue won't be very complicated," Puyol said.
"I am excited about continuing my playing career and if the club wants me I'll stay here."
