Sirino was subject to intense transfer speculation after being linked to Pitso Mosimane's Al Ahly at the end of last season.
The Egyptian side was reported to have tabled a lucrative offer for Sirino's services that Sundowns firmly rejected.
Mngqithi has revealed that although Sirino seems committed to Sundowns, the club would accept an acceptable offer for any wantaway player.
"To be honest, when he came back to training from Uruguay, he looked very interested. He looked committed to playing for the club," Mngqithi said during a media briefing ahead of the MTN8 game against Kaizer Chiefs in Tshwane on Sunday.
"He looked serious about his training, but then, unfortunately, he suffered a knock to his knee, which has kept him out.
"He is back in training this week, but the truth of the matter in terms of the transfer outlook is that he doesn't appear to want to leave.
"I think the club is very clear also in that space that if he has to leave and people are still interested, they must just bring an offer to the table, with the club being very considerate.
"The club does not want to kill Gaston's career, which was very important from the chairman and the board.
"If he no longer wants to play for Sundowns and people are coming with good offers, the club is willing to take them.
"But what is not good is when there is too much talk on what is likely to happen, but nothing really happens.
"At this stage, I think it's a waiting situation, but at the moment, the coaches are very happy with him."
Mamelodi Sundowns are still without defender Ricardo Nascimento who was given extra time off in Brazil due to personal issues.