The Dutch side will pay around €8m for Max, 26, and even with future bonuses the fee will be less than €10m.
Max, one of the Bundesliga’s most productive full-backs, has long sought a move from Augsburg, but has been priced out.
Liverpool and Barcelona previously showed interest, while moves to Borussia Dortmund and Borussia Monchengladbach went up in smoke over Augsburg’s €20m price-tag.
A combination of the Coronavirus crisis and Max pushing for a move means PSV will be signing him at a discount price.
PSV hope to complete a deal for Max, a player they have followed since the start of his career, on Monday.
Max will play a similar left wing-back role to Angelino and Jetro Willems, two players who have left the Eindhoven side in recent years.