The Springboks could face Wales in Washington on 2 June next year.
Wales are looking for an additional fixture ahead of their two-Test tour of Argentina.
‘We are probably going to have an extra fixture on the summer tour next year in the US,’ said Welsh Rugby Union chief executive Martyn Phillips. ‘We are pretty close to getting that done.’
BBC Wales Sport understands the Springboks in Washington is the proposal being looked at.
Wales beat the Boks 24-22 in Cardiff earlier this month.
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