The Premier League stars met Erdogan in London last month with Gundogan handing him a signed Manchester City shirt with the message “to my president”.
German fans took a dim view of the perceived divided loyalty, by booing the pair in a friendly defeat to Austria.
Germany landed in Moscow on Tuesday to attempt to successfully defend their World Cup title and hoping to leave the political controversy surrounding Mesut Oziland IlkayGundogan behind them.
The Germans took off from Frankfurt in pouring rain hoping captain Manuel Neuer will stay fit after eight months on the sidelines with a foot fracture.
Their buildup was dogged by the controversy surrounding Ozil and Gundogan after the players, who have Turkish roots, were booed in pre-World Cup friendlies for meeting Turkish President RecepTayyip Erdogan.