The former Chelsea and Brighton is now in talks with Ajax about taking charge at the end of the season.
But Verweij has questioned why Potter continues to delay committing.
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"What bothers me about Potter is that you can clearly hear and taste that he is okay with Ajax, but would rather go to another club," says Verweij on the De Telegraaf podcast Kick-Off.
If I were in the club management of Ajax - don't worry, that will never happen - I would not want a trainer who only chooses Ajax if he does not receive any other offers. You have to choose a trainer who is eager to start working at Ajax."
His fellow journalist Valentijn Driessen also criticises Potter: I just get the strong feeling that he is almost using Ajax and now also Feyenoord to put pressure on Manchester United, for example, where he really wants to go. Is this the way to play it?"