The news comes after Partizan crashed out of Europe following a 1-1 draw with Marseille, despite being gifted a goal by an error from another alleged United target Daniel van Buyten.
Matthaus had been linked with the managerial job at CSKA Moscow, but instead has accepted the position of national team coach with Hungary.
"The Hungarian team has lots of potential, that is why I decided to accept this job," said the German.
"Our main goal will be to get back to the World Cup again after 20 years."
A two-year contract with the Hungarian FA should rule him out of the running to take over from Sir Bobby, if he was ever under consideration anyway.