The 21-year-old spent last season away from Schalke on loan in Belgium at Cercle Brugge, where he clocked regular game time.
Schalke are willing to let the former Manchester City youth player depart this summer and Rangers are pushing to take him to Ibrox.
And Schalke have allowed Matondo to skip travelling to their training camp in Austria on Monday, according to German broadcaster Sport1.
They are keen to allow the Wales international to clarify his future and further negotiations over his move away from Schalke will be held at the beginning of the week.
It is suggested that all parties concerned expect Matondo to complete a move to Rangers, but personal terms have not been fully agreed.
Schalke are expected to receive a fee of around €3m from Rangers for the 21-year-old.
Rangers have already made additions during this summer’s transfer window as they look to wrestle the Scottish title away from Celtic next season.
