The incidents come at a sensitive moment with a crucial El Clásico clash against rivals FC Barcelona fast approaching.
Tensions first surfaced in April when Germany international Rudiger reportedly clashed with a teammate during training adding to frustration after their Champions League exit to Bayern Munich.
Although he later apologised and attempted to repair relationships by hosting a team lunch, the incident left a lingering impact.
Meanwhile, French star Mbappe became embroiled in a dispute with a member of Álvaro Arbeloa’s coaching staff, reacting angrily to an offside decision during a training drill, intensifying concerns over internal tensions.
Real Madrid are second in the Spanish topflight table having accrued 77 points from 34 outings.