The Uruguay international was conducting an interview ahead of the Copa America and was asked by the reporter if he could obtain a shirt from Son, whom the journalist referred to as "the Korean one".
After Bentancur replied "Sonny?", the reporter responded "or any other champion", to which the former added "Or any cousin of Sonny, they all look more or less the same!".
Bentancur's ill-judged remark drew enormous criticism online, and the former Juventus midfielder quickly posted an apology to Son on Instagram, insisting that he never meant to offend his captain.
Neither Spurs nor Son commented on the incident for a few days, but both released statements on Thursday morning, in which Son affirmed that he forgave his teammate for his "mistake" and wanted to draw a line under the incident.
Bentancur 'could miss start of next season'
Meanwhile, Tottenham confirmed that all players would receive further diversity education in the wake of Bentancur's comment, but the South American could now land himself in hot water with the authorities.
According to football.london, the FA are now looking into Bentancur's remark, although they are yet to decide whether to charge the 26-year-old with a breach of their rules.
However, should the governing body see fit to charge Bentancur, the midfielder would be at risk of a fine or a possible ban of unspecified length, potentially ruling him out of the start of Tottenham's 2024-25 season.
The report adds that Spurs are still dealing with the matter behind closed doors, although their overall response could be dictated by the outcome of the FA's investigation.
Bentancur's initial statement of regret was posted on an Instagram story, but the Uruguayan uploaded a new permanent apology to his socials on Thursday, accompanied by an image of him in action for Tottenham.
Bentancur insists "all has been clarified" with Son
"I would like to communicate to all fans and everyone who follows us that after my interview where I referred to Son and no one else, I have spoken to him and, logically given our deep friendship, he understands it was only an unfortunate misunderstanding. All has been clarified and solved with my friend," Bentancur said.
"If someone felt offended because of my words through this media tool I would like to offer my sincere apologies. But I also would like you to know that never, never I referred to anyone else. Only to Son and for that reason I've never had the intention to offend directly or indirectly anyone. A big hug and all my respect to everyone."
In November 2019, Manchester City's Bernardo Silva was banned for one game and handed a £50,000 fine for a tweet comparing then-teammate Benjamin Mendy to the mascot of Spanish confectionery brand Conguitos, being charged with a breach of FA rule E3(1).
One year later, Edinson Cavani - then playing for Manchester United - was suspended for three games and fined £100,000 for using the word "negrito" in an online post, but Alejandro Garnacho escaped punishment for accompanying an image of Andre Onana with two gorilla emojis in November; the goalkeeper insisted that his teammate was referring to his "power and strength".
Tottenham travel to Leicester City in their opening game of the 2024-25 Premier League season on August 19, before hosting Everton on August 24 and travelling to Newcastle United on August 31.