Sky Sports revealed on Friday that the Royals were set to make an offer to the 23-year-old centre-half.
Sunzu, who plays his club football for Congolese outfit TP Mazembe, is currently away on Africa Cup of Nations duty.
He was, however, released from the Zambia camp to train with Reading last week and did enough to earn himself a deal.
He is now waiting for news on the completion of a switch, with a fee in the process of being agreed.
"Everything went well," Sunzu said of his spell in England.
"I'm happy because I passed the assessment and now it's up to TP Mazembe and Reading to finalise the deal.
"When they do that, I will sign the contract right here."