Sirino is believed to be wanting out of Sundowns to reunite with former coach Pitso Mosimane to Egyptian giants Al Ahly.
Meiring suggests the 30-year-old Uruguayan should be let go to avoid breaking the team's spirit in the DStv Premiership winning squad.
"Of course they must let him go, man. There is no player bigger than a team. Before him there was Sundowns," Meiring tells snl24.com/kickoff.
"After him, there will be Sundowns, and he must go wherever he wants to go. Because his heart is not there at Sundowns. Because for him to do all these things...
"I understand from his part he wants to play for somebody that he will free with and all that, but it looks like he has a connection with Pitso...So let him go.
"Now you gonna have an unhappy player, he's gonna bring problems in the team, you know how players are. So the best thing is they must let him go and use the space for somebody else. Percy Tau was in a different class and is local, and he never had that attitude.
"Sundowns had Tau who I believe was Sundowns' best player then, but Sundowns survived after him. So you know what? Sirino must go then. Somebody else will come."
Sirino scored five goals and registered three assists in 27 games across all competitions last season after the long protracted transfer saga with the Red Devils.