Ansu, 20, has made 38 appearances in all competitions under coach Xavi Hernandez, but 27 of them have come as a substitute.
Bori Fati -- who manages his son's career alongside agent Jorge Mendes -- said Ansu deserves more minutes and has pledged not to return to Camp Nou to watch a match until the situation changes.
"If it was up to me, I would take him [to another team] but [Ansu] wants to stay at Barcelona," Bori told Cope on Tuesday.
"He does not want to sign for another club, but I want to see him succeed. As a dad, I am angry. Seeing Ansu play so little winds you up a little bit and sometimes I think as a father, not a coach."
Ansu broke into the Barca team at the age of 16, breaking appearance and goal scoring records in LaLiga and the Champions League, but a series of unfortunate injuries saw him miss most of the previous two campaigns.
However, he has remained fit throughout the season, with Bori adding that he is "more explosive than ever" when confident and just lacking rhythm and games.
The situation led to Bori calling a meeting with Barca sporting director Mateu Alemany and Ansu's agent Mendes this week.
"I called Mateu," he added when asked who set the summit up. "He told us that Ansu is part of the club's heritage and they have bet big on him.
"As a dad, I think differently, maybe I am wrong. He is your franchise player, the No.10, he took [that number] on when no one was ready to take it from [Lionel] Messi.
"What annoys me is how they're treating him in terms of minutes. One minute, two, three... I am not asking for him to be a starter whatever, because all the forwards at the club are phenomenonal, but we are talking about Ansu Fati, of Spain and Barcelona, who came through La Masia... if you don't give him [a chance], who will you?
"If it carries on like this, I will go [back] to [the family home in] Seville and that's that. I didn't go to the game against [Real] Madrid. I won't go to the stadium anymore. The other day Ansu asked me why I didn't go, he thought I was there. I told him I didn't fancy it."
Despite his own grievances, Bori says Ansu remains content and prepared to keep fighting for his place in a Barca side that are 12 points clear at the top of LaLiga.
"Ansu is perfectly fine," he said. "How could he be depressed when he has so much family around and people to talk with? He comes home from training and is happy. When Ansu is happy, no one can stop him. You will see that."