The defensive duo could face Los Che having successfully completed first-team training, while Thiago Alcantara is in contention to play as well
The defenders missed the Blaugrana's 2-1 defeat to Real Madrid in the Spanish Supercopa on Wednesday evening, as Tito Vilanova's side lost the tie on away goals.
Nevertheless, Alves, who was sidelined due to an edema in the femoral biceps in his right leg, has trained with the first-team on Saturday, ahead of the meeting with Los Che.
Meanwhile, club captain Puyol, who has been nursing a cheekbone injury, sustained in the victory over Osasuna last weekend, has also returned to training, though he is likely to start from the bench.
Tito Vilanova will have a full squad to pick from, having been dealt a further boost as Thiago Alcantara returns from a tibia injury which has sidelined him for much of pre-season, and also the Olympic Games with Spain.
Sunday's La Liga encounter against Valencia kicks off at 21:30CET.