Sunzu, 23, was given permission to be released from Zambia's Africa Cup of Nations squad to train with the Royals in the past week and impressed in a game on Thursday.
He said: "Everything went well. I'm happy because I passed the assessment and it's now up to TP Mazembe and Reading to finalise the deal. When they do that, I will sign the contract right here."
Two possible stumbling blocks to the deal could be TP Mazembe's £4m valuation of Sunzu and Arsene Wenger's interest in the player, says the Sunday Mirror.