Fabregas has been the subject of two failed bids from United so far this summer and reports have claimed that the Premier League champions are considering lodging a third offer of £35million.
Barcelona have previously insisted that Fabregas is not for sale and that all bids for the former Arsenal captain would be rejected.
New Barcelona coach Martino has discussed the issue with Fabregas and confirmed the Spain international is a key part of his plans for the coming season.
"I have spoken with Cesc and he told me what he thought," Martino told a press conference after Barcelona thrashed Santos 8-0 to win the Joan Gamper trophy on Friday night.
"The idea of not counting on him doesn't enter my mind, but the player also has to decide.
"I dare to say that he will stay."
The 26-year-old's team-mate Javier Mascherano told Sky Sports News earlier this week that he believes Fabregas is happy at the Nou Camp.
"I didn't talk to him but I think he is happy," said Mascherano. "It is difficult when you have to speak about the personal situation of other players because sometimes you don't know what they think.
"I see him here training and he is happy. He grew up in Barcelona and feels the call of the shirt.
"It is difficult when you grow up here to leave because Barcelona is a big team, a big city, really nice to live in and all his family is here.
"I think he is a really key player for us and I think the coach and the people who work here want to keep him."
Talking to Sky Sports News last week after Barcelona's friendly defeat at Bayern Munich, Song told Sky Sports News "I did not speak with him but I know Cesc is 100 per cent here.
"He loves Barcelona, he loves the club. He will stay here next season and give 100 per cent because I know him very well and he'll want to fight. He's focused on the club.
"He wants just to give his best for Barcelona. He's from Barcelona, he loves Barcelona and he'll want to start the season to show what he can do.
"People are talking and talking, but we know he is focused here and ready to start the season. It's my own opinion but I know he will stay here, 100 per cent."
However, United goalkeeper David De Gea says his fellow Spaniard would 'greatly improve' David Moyes' squad.
"He will have to make the decision whether he wants to stay or join us," De Gea told the Manchester Evening News. "It would be a very good signing and he would help us improve greatly."
Fabregas has been mooted as an ideal replacement for the retired Paul Scholes and the former United midfielder would welcome his arrival at Old Trafford.
"Well, it would be nice to sign a player of that quality," he told Sky Sports News.
"He's proven in the Premier League, obviously he's with Barcelona, it's a big club, it will be difficult to get him away from there.
"But if you do, you have to fancy your chances strongly that we can go on and be successful with a player like that in your team."