The club will be offering the South Korea international counselling, according to the Evening Standard.
Son was seen crying on the pitch at Goodison Park after seeing the extent of Gomes’ injury.
He was described “as though, mentally, he wasn’t in the room” when the Spurs players were getting ready to leave the dressing room after the match,” added The Athletic.
Gomes was tripped by Son in the second half of the Premier League clash between Tottenham and Everton.
He subsequently collided with Spurs right-back Serge Aurier, which caused the injury.
Gomes received treatment on the pitch for around 10 minutes, before being stretchered off.
Everton confirmed on Sunday night that the Portugal international had suffered a fracture and dislocation to his right ankle. He’s set to have surgery on the ankle on Monday.
Son was initially booked for the challenge, but as the damage to Gomes’ ankle became clearer, referee Martin Atkinson changed his mind, and brandished a red card.
Both Son and Lucas Moura were the first players to notice Gomes’ broken ankle, and were both seen immediately putting their hands on their heads.
The midfielder was then swarmed by players offering support while he received treatment.
Son had to be consoled by both Tottenham and Everton players on the pitch, before he was shown the red card.
After the match, team-mate Dele Alli told Sky Sports that Son was “crying so much he can’t even keep his head up”.
Captain Ben Davies also reportedly tried to console Son in the dressing room, but sat back down after he didn’t get a response.
After the match, Mauricio Pochettino confirmed that Everton captain came into the Tottenham dressing room to console Son.
“I want to thank the captain, Seamus Coleman. He came into the dressing room to console Son,” said Pochettino after the match.
“I think Son is devastated because of the consequences.
“I want to send my best wishes to Gomes. What’s important now is that he recovers well.”