Erasmus has been coaching for only two years, but who led his side to their first Currie Cup title in 29 years in his first year in charge before sharing the title this year with the Blue Bulls.
"It sounds good when there are rumours of this kind (coaching the national team), but until that happens I will earn my bread and butter at the Free State," he told Die Volksblad.
"I am now concentrating on the Cheetahs' Super 14 campaign and am throwing my full weight behind it."
Erasmus helped Jake White with analysis before the two England Tests and said he enjoyed the challenge.
"Jake and I discussed the analyses over the telephone," Erasmus said. "All I did was to make one or two suggestions about things I had noticed.
"I can't accept any credit for the victories in the last two tour matches, but it was nice to be able to help.
"I believe the Springboks themselves turned things around after their defeat in the first Test.
"I, just as the rest of South Africa, want the Springboks to win. The way they played in those last two matches made me think we have a chance at the World Cup tournament in France next year."
Erasmus said he would consider assisting White if offered the job as assistant for the World Cup.
"I'll do anything to help the Springboks win because I am also a supporter, as all the others who stand behind them, but there are many factors to be considered.
"I am involved in the Super 14 and Currie Cup competitions, my family and my home are here and I have a three-year contract with the Free State. That is where my priorities are now.
"My family and I planned what we were going to do in these three years. There are many things to be discussed, but it will be a great honour if they (SA Rugby) invite me.
"If it does not happen, I will remain with the Free State and maybe it will happen in the future."