Williams, a former New Zealand heavyweight champion, was unbeaten in seven professional fights between 2009-15. Parker sparred with Williams before Williams' fight against Clarence Tillman in 2012, the year Parker turned professional, and the rugby player more than held his own.
Williams' last fight was against Chauncy Welliver, a bout he won by decision. His most infamous fight was against Frans Botha in Brisbane in 2013.
Williams won it by decision after 10 rounds, but veteran Botha complained bitterly that it had been scheduled for 12 rounds and that it had been cut short because he was getting the better of Williams.
That fight appeared to be a reality check for the now 32-year-old, who had negotiated a "boxing clause" in his contracts with New Zealand Rugby.
Williams is contracted with NZ Rugby until the end of next year.
Parker has several big supporters among the All Blacks, including Israel Dagg, who walked to the ring with him before his IBF title elimination bout against Carlos Takam in 2016.
Parker told ESPN that he hoped Dagg and others could travel to Cardiff in support, but given the players' Super Rugby commitments, it's probably unlikely.
"I think some of the players might be free and might come over," Parker added. "I'm good friends with Jerome Kaino, Israel Dagg, Sonny Bill. I think if some of them do get time off they'll definitely come over and support.
"This is a fight where I think the whole of New Zealand are going to back us, and it can be a fight where we do well. It's going to put New Zealand boxing on the map and it's going to put us in the history books."
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