The Welsh international has been in talks over a move to Ibrox from Schalke 04.
Matondo would become the club's fourth summer recruit after the arrival of John Souttar, Antonio Colak and fellow Welshman Tom Lawrence.
The fee for the 21-year-old is understood to be around €3million.
He has been contracted to Schalke since 2019 when the German giants spent a reported £11million to land the attacker from Manchester City.
Matondo has made 32 appearances for Schalke, while enjoying loan spells at Stoke City and Cercle Brugge in the Belgian top-flight.
The player will be hoping to be part of the Wales squad at the World Cup in Qatar.