The Croatia international forward had said earlier this summer that he was going to leave Bayern after two seasons at the Allianz Arena.
The signing of striker Robert Lewandowski on a free transfer following the end of his contract at Borussia Dortmund means that there will be more competition for places for Mandzukic.
Sammer has now stated that Bayern have reached an agreement with the Spanish champions to sell them the 28-year-old striker.
"There is a verbal agreement between Atletico Madrid and Bayern Munich, as well as between Atletico Madrid and Mario Mandzukic,” he told Deutsche Presseagentur.
“Although nothing has been signed yet, I believe that we all will stay true to our words.”