He said he would apply his mind to whether the sports bodies have complied with all the requirements, "and after consultation with the minister of health, the minister will then give a go ahead for the PSL to train".
He said sports bodies had been informed in writing of the process.
The PSL had been hoping to finish the season by July 31 but it now seems unlikely.
There will simply not be enough time for teams to conduct training camps and play the 107 remaining games within the next 40 days.
Mthethwa said his department is not in a position to advise the PSL on how to deal with the July 31 deadline.
"The issue of possibility as to whether the leagues could be finished in this current season or not depends on the PSL. the leagues can make their own decision.
"The possibility of finishing is dependent on what happens with the Covid-19 pandemic and guided by government's overall risk-adjusted strategy," he added.
"Of uppermost importance is to protect the lives of the citizens, players and all those involved in football and sport in general."
Reports have suggested the PSL is looking at hosting the rest of the programme at one venue, either in Johannesburg or Durban.
Minister still assessing PSL's action proposal
The Premier Soccer League (PSL) will need to provide further assurances to the minister of sport, arts and culture Nathi Mthethwa before training can resume and, moreover, satisfy the health department that players will not be at risk from the coronavirus.
The PSL has for the past week been waiting for Mthethwa to give it the green light for teams to return to training.
The football body submitted its plans a fortnight ago on the Covid-19 compliances it will put in place for teams to follow.
In an e-mailed response to Sowetan, Mthethwa detailed what was delaying the resumption of training among PSL players.
"The department is assessing the plans submitted by sport federations after the gazetting of the directives on 11 June," Mthethwa said.
"Approval is not automatic. It depends on a number of factors, such as completeness of the plans, the adequacy of supporting information, etc."
He said he would apply his mind to whether the sports bodies have complied with all the requirements, "and after consultation with the minister of health, the minister will then give a go ahead for the PSL to train".
He said sports bodies had been informed in writing of the process.
The PSL had been hoping to finish the season by July 31 but it now seems unlikely.
There will simply not be enough time for teams to conduct training camps and play the 107 remaining games within the next 40 days.
Mthethwa said his department is not in a position to advise the PSL on how to deal with the July 31 deadline.
"The issue of possibility as to whether the leagues could be finished in this current season or not depends on the PSL. the leagues can make their own decision.
"The possibility of finishing is dependent on what happens with the Covid-19 pandemic and guided by government's overall risk-adjusted strategy," he added.
"Of uppermost importance is to protect the lives of the citizens, players and all those involved in football and sport in general."
Reports have suggested the PSL is looking at hosting the rest of the programme at one venue, either in Johannesburg or Durban.