Chelsea have begun contract talks with the teenage defender, who has less than a year left on his present term.
Cucurella, meanwhile, could leave the club just a year after coming for a rumored sum of up to £63 million.
Last season, the Spain international made 33 appearances for Chelsea, including 24 in the Premier League.
He played both as a centre-back and as a wing-back for the Blues, who finished 12th.
Cucurella was an unused substitute in Chelsea’s season-opening win over Liverpool, while Maatsen came off the bench late in the game.
Maatsen played last season on loan at Burnley, and the newly promoted Lancashire club had a £15 million bid for his services rejected.
His strong pre-season performances at left-back, wing, and playmaker altered Pochettino’s mind and may have revitalized his Stamford Bridge career after repeated loan spells abroad.
Chelsea will shortly announce the completion of numerous high-profile sales this summer, with stars such as Kalidou Koulibaly, Edouard Mendy, and Kai Havertz all departing for large sums.