Iniesta, 32, was initially ruled out for between six to eight weeks after suffering a knee ligament injury in the 3-2 victory over Valencia on 22 October.
The Spain international returned to training ahead of schedule on Friday (25 November), however, seemingly leaving him in the frame to return in time for the visit of Zinedine Zidane's side on 3 December.
Umtiti meanwhile suffered a muscular injury while playing for France during November's international break, with tests initially predicting he would be sidelined for three weeks.
But speaking at a press conference ahead of Sunday's La Liga clash at Real Sociedad, Enrique spoke positively about both players, insisting a final decision will be made by the team doctors within the next week.
"I am optimistic about getting them back, when depends on how the players develop, but yes both are doing very well," Enrique said. "Andres has been training for a couple of days now, that is very good news. He has done some work with us but there is still more to be done. Exactly when they come back depends on how they and the doctors see things."
Gerard Pique meanwhile suffered a minor knock in the comfortable Champions League win over Celtic on Wednesday with reports in the Spanish press suggesting the centre-half will be a doubt for Sunday's game at the Anoeta Stadium. Pique trained with the group as normal on Saturday morning however with Enrique insisting there was nothing to be concerned about, suggesting he could even play this weekend.
"Gerard Pique is normal, it is a normal recovery process. He took a knock two games ago so the players come in and do different kinds of work, it all depends on how things are developing.
"There is nothing really to be concerned about Pqiue, it is a contact sport and players take knocks, sometimes they have to play carrying some kind of pain, it doesn't necessarily mean that he can't play tomorrow."
Barcelona travel to San Sebastian knowing that if Neymar picks up a yellow card playing against Real Sociedad, he will pick up an automatic one-match ban having already been booked four times in the league this season. Despite a suspension looming over the Brazil superstar, Enrique insists he will not pull the player out of the firing line this weekend.
When asked if he would consider leaving Neymar out on Sunday, Enrique responded: "No, not at all. We get the same points in Sen Sebastian as we would for beating Madrid, three points, so absolutely not."