The Premier League champions have made two offers for the former Arsenal midfielder, for a reported £25million and £30m, both of which were rejected by the Catalan club.
On Thursday United manager David Moyes told reporters that negotiations for Fabregas were "ongoing" but Martino, speaking in his first press conference as coach of Barcelona, insisted the player was staying at Barcelona and was part of his plans.
He said: "I'm not going to involve myself in the club's accounts, but considering the club has already rejected two offers, I would guess it will reject a third. In other words, he will remain here."
The Argentinian coach's words were backed up by vice-president Josep Maria Bartomeu, who said: "It's logical that we've had offers for Fabregas because he is a quality player, but he is not for sale."
The 50-year-old coach succeeds Tito Vilanova, who resigned from the role last Friday to continue his battle with cancer, and the Argentinian began his press conference with a message for his predecessor:
"I'm very proud to join this institution, with its illustrious history, but regrettably, I know why I'm here and I'd like to take this opportunity to send my best regards to Tito," he said.
"We don't know each other but we spoke on the phone and he welcomed me to the club and wished me good luck, and I wished him a speedy recovery."
Martino has spent his 15-year managerial career in South America, coaching a host of Argentinian club sides, most recently Newell's Old Boys, where he spent the majority of his playing career, plus the Paraguay national team, who he led to the World Cup quarter-finals in 2010 and the Copa America final in 2011.
Asked if he would be able to cope with the pressure of coaching in Europe, Martino said he agreed with the last Argentinian coach to take charge of Barcelona, Cesar Luis Menotti, who once remarked: "Once you have coached in Argentina, everything else is much easier."
Martino said: "Coaching in Argentina is not easy, there are no comparisons between these countries, but we feel the same pressure. I don't have the career Menotti had so I am less qualified to say that, but I share his opinion."
And he is under no illusions as to what is expected of him at the Camp Nou, adding: "It's logical that this club has to win trophies. I would be a failure if we didn't.
"Sometimes the team that wins doesn't deserve to, but Barcelona are used to winning and we will have to keep doing that."
He added that it was "natural" that many Barcelona fans did not know much about him, considering he has only worked in South America, but pledged to adapt quickly to the club's traditions and philosophy.
He indicated this included honouring the club's famed academy, which has produced the likes of Lionel Messi, Andres Iniesta, Xavi, Sergio Busquets and Victor Valdes.
"Barca has the same idea of its academy as the club I grew up in and spent most of my career at [Newell's Old Boys], so I'll be delighted to support the first team with players from the academy," he said.
"Of course I will contemplate the style of the club and the style of the players and continue with that because that's what they are comfortable with.
"I will adapt to the club, as well as contributing my ideas in order to make the team much more complete."
He added: " I will try and make sure the players retain their hunger and if I can do that, we will have many great years ahead of us. "
In his final press conference at Newell's, Martino said he believed that his compatriot Messi, who is also from Rosario, influenced the Barcelona board's decision to appoint him, something the player later denied.
The coach sought to explain the situation: "I said that they may have consulted him, but that wasn't the case because he has said so and I can't contradict him. He doesn't need special praise or attention, he's always in great form because he's the best player in the world."
And he dismissed the suggestion that Messi would be unable to play alongside Brazil forward Neymar, who joined the club for 57m euros (£49m) in June.
"I don't understand why two players of that quality can't play together, but if they can't, it will be my fault, not theirs," he said.