The police have agreements with three labour unions on promotions.
IOL reported that a memorandum said some specialised units had allegedly promoted their constables to warrant officers, "while station members are left behind".
South African Policing Union (Sapu) general secretary Tumelo Mogodiseng previously said the union supported the strike.
"We want to put it on record: we acknowledge and have made members aware of the fact that the police are categorised as an essential service and therefore not allowed to engage in industrial action."
During the media briefing on Thursday, Sapu president Mpho Kwinika asked officers not to strike.
"Is there going to be a strike on Monday? I don’t know. We have spoken to them [members] that they should not strike ... there are better avenues that they can use. They can assemble and demonstrate, but with the element of peace."