Phala had been staying away from the club's training sessions since the opening of the transfer window as he tried to force a move to Johannesburg.
With the window now closed, the 32-year-old is said to be prepared to accept any decision taken by the club on his future, including finishing the season with the Tshwane giants.
The former Bafana Bafana player still belongs to SuperSport, with his contract set to end in June 2019.
Speaking to this website, the player's mother Suzan Phala reiterates that her son is still a SuperSport United player.
"Yes, the deadline has passed, Thuso has no [new] team. Esiyikhulumayo... Thuso is still a SuperSport player," she tells KickOff.com. "He is not training with SuperSport but he's still contracted to SuperSport."
Asked what is next for her talented son, the former Platinum Stars administrator adds: "There is nothing we can do. There is nothing that is gonna happen next, he is a product of SuperSport United, it remains like that.
"He is not going back to training as Stan [Matthews] says they don't want him, that's what yesterday's paper says... that's at least what they say in the papers. If they cannot allow him to go anywhere, it gives him no choice."
SuperSport's David Sikhosana says it is all up to coach Kaitano Tembo whether he fields the player as he is still on their books.
"Phala is with the team, he is still our player. It depends on the coach. I didn't go to training today so I don't know if he is there," Sikhosana adds.
"Remember, we were not playing this week so we only start training today, so I'm not yet there. Last week it was a busy, busy week. Because we were not playing last weekend, we gave them a day off, there was no one."
A reliable source at SuperSport confirms that the player did not show up at the club's training ground on Monday.
Phala has played only 11 times for Matsatsantsa this season, six in the league, two in the Telkom Knockout (scoring one goal), and three times in the MTN8.