At just 25 years of age, highly-rated winger Draxler still has time on his side when it comes to fulfilling his potential.
He is not considered to have achieved that feat just yet, despite spending two-and-a-half years with Ligue 1 champions PSG and earning 49 caps for his country.
“Julian is a talented player, but he has never really exploited his potential. He lacks character to meet expectations at the highest level.
“In Paris, there was the opportunity this season for him to seize his chance and prove his worth during the long periods of unavailability of Neymar and Edinson Cavani, but he was too disappointing, especially in the big matches in the Champions League. He could do a lot better.”
Pressed on where Draxler has disappointed the most, World Cup winner Brehme added: “In his finishing.
“Whether in the league or Champions League, he has had many opportunities to score, but lacks composure in the final moment and I feel that has complicated things. He lacks certain simplicity in his game.”
Draxler has made over 100 appearances for PSG and recorded 20 goals, landing a number of major honours along the way.
He does face fierce competition, though, when it comes to attacking berths at Parc des Princes.
With that in mind, and the need to find consistency, Brehme believes another change should be made in 2019.
Asked if he should stay at PSG, Brehme said of Draxler’s future: “To do what? He cannot win because of formidable competition and if he is still ambitious, it is better to leave.
“In any case, I do not see him coming back to Germany.”