Media reports in Brazil claimed that Flamengo would pay €3 million (£2.3m) to secure the playmaker's services on a season-long loan, and that Wolfsburg's main sponsor Volkswagen, would chip in with half of his wages.
But Magath has told the player he will be attending pre-season at the club after he returns from knee rehabilitation in his homeland.
“I expect him back fit and healthy,” the 58-year-old told Bild.
“We want him to be fully fit by July 31. It is clear that he is no longer on the market. He will be staying with us.”
The 27-year-old was farmed out on loan to Atletico Madrid last season and played a major role in their Europa League triumph.