The defender, who was also linked with Arsenal, is expected to undergo a medical with the Premier League club in the coming days.
Sunzu, 23, currently represents TP Mazembe but will likely link up with Reading following Zambia's defence of the African Cup on Nations in South Africa.
He has been released from Zambia's pre-tournament camp to finalise his move to the Madejski Stadium.
“Sunzu is heading to Reading for tests after the agreement by TP Mazembe and the Zambia Federation," said Mazembe president Moses Katumbi.
“He just sent us a message in which he thanked the club.”
Sunzu spent a spell on trial with Reading earlier in his career, with manager Brian McDermott recently describing him as a "good lad".