Pirates are currently being held 2-2 by Golden Arrows in a thrilling game at the Moses Mabhida Stadium.
Bucs scored first through Lucky Lekgwathi, but two quickfire goals by Dillon Sheppard and Katlego Masgeho gave Arrows - and Swallows - the advantage.
Siyabonga Sangweni equalised for Pirates, but Swallows, who are being held 0-0 by Maritzburg United, need just one goal to take the title.
Elsewhere, Black Leopards are leading Ajax Cape Town 1-0, meaning the will be safe if it stays this way. Santos are goalless against Jomo Cosmos.
Kermit Eramus and Sibisuso Zuma have given SuperSport United a 2-0 lead against Bloem Celtic, while Wits are leading 2-0 against Platinum Stars.
Kaizer Chiefs vs AmaZulu and Sundowns vs Free State Stars are still goalless.