Martino has come under pressure in recent weeks, with Barca's La Liga title defence stuttering badly after three defeats in quick succession.
Losses to Valencia, Real Sociedad and Real Valladolid in their last seven games have left the champions four points off Real Madrid, though the sides will contest El Clasico on Sunday, with Barca desperate for points.
With the added weight of the Camp Nou job reportedly getting to the Argentinian, talk of his departure has mounted, but Barca's marketing vice-president Manuel Arroyo was quick to downplay such rumours at a press conference on Monday.
He said: "We found out a few minutes ago that this news was emanating from somewhere.
"We don't support it, Tata (Martino) is contracted to the club and in this week that is so important to us he is dedicated to Barca.
"We asked him and he has flat out denied it. He has not spoken to anyone, including his staff, it's completely false."
When asked about claims Martino's contract includes a clause that would make him free for the Argentina post, Arroyo added: "I can't give you the exact date, but they're practically habitual. It is a clause that exists not only for him but also for us, but I insist, there is no intention to invoke it.
"He hasn't said that he's going to continue, but we are all working towards the future together, more so in this very important week for the club ahead of our trip to the Bernabeu."
