Cape Town - Wales are exploring the possibility of playing the Springboks in June 2018 ahead of their two Test tour to Argentina.
The fixture could be played on neutral turf in Washington, USA, on Saturday, June 2.
Welsh Rugby Union chief executive Martyn Phillips refused to name the country national coach Warren Gatland's side would face, but confirmed it would not be the host nation.
"We are probably going to have an extra fixture on the summer tour next year in the US," said Phillips.
"We are pretty close to getting that done."
BBC Wales Sport understands the Springboks in Washington is the proposal being looked at.
Wales last played South Africa earlier this month in the final game of their autumn series, winning 24-22 in Cardiff.
Nothing has yet been finalised but Phillips believes the third summer game would fit well ahead of two Tests in Argentina on June 9 and June 16.
Ireland have already played in the USA, when they famously defeated the All Blacks 40-29 in Chicago in November 2016.
The Springboks face England in a three-Test series on June 9, 16 and 23 so the possible match against Wales would serve as a warm-up in what would be current coach Allister Coetzee's - or whoever is in charge of the Boks at the time - first assignment of 2018.