Martino announced he is to leave Camp Nou after just one season in charge following Barca's 1-1 draw with Atletico Madrid on Saturday, which gave the capital club their first top-flight title since 1996.
Former Barca midfielder Enrique is expected to succeed the Argentinean next season, having confirmed he will leave Celta Vigo during the week.
But speaking after Celta's 2-1 loss at Valencia, the 44-year-old remained tight-lipped on his future plans.
"When I have something to say, I'll tell you," Enrique said. "Right now, I can't make anything up.
"We'll see if there's anything or if there isn't anything and in this case, something else.
"I saw (Barcelona's draw to lose the Liga title), I suffered and I think that Atletico Madrid are the worthy La Liga champions."
