The Germany international is coming off contract at Borussia Dortmund and set to leave this summer.
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The 29 year-old wants to leave the Bundesliga and test himself abroad.
Contact has been established between Arsenal and Brandt, though Atletico have now entered the picture.
Marca says Atletico are making their move, seeing Brandt as a an ideal replacement for Antoine Griezmann.
Griezmann has agreed to join Orlando City of the MLS at the end of the European season.