Cubarsi, 17, has been an ever-present for Barcelona since January, making 13 appearances for the Catalan giants this year, while he debuted for Spain against Colombia on Friday night.
The centre-back has a contract at Camp Nou until June 2026, but it is believed that his release clause is around €10m (£8.5m), and he is not able to sign a professional deal until he turns 18 early next year.
A recent report claimed that Man United are keen on the former Girona youngster, with the Red Devils closely monitoring his rise to the first team.
Meanwhile, Manchester City, Arsenal and Chelsea are also believed to be admirers of a player who picked up the Man-of-the-Match award for his display in Barcelona's Champions League last-16 second leg with Napoli before the March international break.
According to Marca, Barcelona have offered Cubarsi the chance to improve his salary immediately, with a long-term contract then being offered when he turns 18.
The report claims that the Spaniard is likely to be offered a new deal until June 2030 or June 2031, and he is keen to remain at Camp Nou despite the speculation surrounding his future.
Cubarsi is allegedly not prepared to accept any offer, though, and will ask 'to earn what he deserves', having quickly developed into an important player for Barcelona.
Barcelona boss Xavi lavished praise on the defender following his display against Napoli in the Champions League.
"Cubarsi is a very rational kid, a humble guy, calm, down to earth. He has an incredible future, we're probably looking at a centre-back who will play at the maximum level for years to come," Xavi told reporters at the time.
"My pulse does not go up when Cubarsi has the ball. That's the best summary for him. Cubarsi does not get nervous. He's very calm, his ball output is brutal, he has pause, he generates attacking plays, he links up with interiors and forwards. It's a spectacle to watch him play."
Cubarsi became Spain's youngest-ever defender when he debuted against Colombia, breaking the previous record, which had been held by Sergio Ramos.
"I'm very proud of my debut as it was a dream I've had since I was a kid. I'm grateful for the coach's trust and I will try to make the most of it by giving my best. I always try to be me and play calmly," he said after featuring for his country.
Man United are also believed to be tracking Barcelona B defender Mikayil Faye ahead of this summer's transfer window.