United coach David Moyes said on Thursday the English champions had not given up their pursuit of Fabregas, who returned to his boyhood club in 2011 after eight seasons with United's Premier League rivals Arsenal.
"Obviously I am not going to get involved in the club's economic affairs but they have already rejected two offers so I will add a third," Martino said at his first news conference since he was appointed to succeed Tito Vilanova on Tuesday.
"We are going to keep him here," added the Argentine, a former coach of Paraguay and most recently Newell's Old Boys in his native Rosario.
Barca vice president Josep Maria Bartomeu also ruled out selling Fabregas, saying it was normal for United to be interested in the 26-year-old as he was "a great player" but that the club were counting on him.
Barca hired Martino after Vilanova was forced to step down due to illness as he is known to favour the club's possession-based playing style.
The silver-haired 50-year-old said his immediate priorities were to get to know the squad and coaching staff and make sure the players retained their hunger for success.
He would be focusing as well on making sure Barca's World Player of the Year Lionel Messi, who is also from Rosario, was able to continue his phenomenal scoring run of recent seasons.
"What we are going to try to do is make him feel as comfortable as he has up to now, making him feel good in the team," Martino said. "With that he will do the rest."
One thing Martino said he would be working on was making sure Barca pressured opponents high up the pitch and that they were comfortable defending a long way from their own goal.
He will have a first chance to test his theories with his new charges when Barca play a friendly at Polish side Lechia Gdansk on Tuesday.
(Reporting by Iain Rogers, Editing by Clare Fallon)
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