Magath worked a near-miracle last season to take Schalke to the verge of the Bundesliga title as they finished second behind champions Bayern Munich, but he has a reputation for being a hard taskmaster.
Having finished eighth in 2009, Magath reorganised the Royal Blues and earned a Champions League place for this season. He has a contract until 2013.
His success at Schalke, where he has transformed a club crippled by financial problems, has mirrored the miracles he achieved in taking little-fancied Wolfsburg to their first Bundesliga title in 2009.
Having sold Germany defender Heiko Westermann and released a group of players, Magath has been repeatedly criticised by Schalke's fans over his style of management and defended himself at Thursday's press conference.
“It is beyond me that this is going on now, just before the start of the new season,” said the 57-year-old who has signed Spain striker Raul and Germany defender Christoph Metzelder for the new season.
“I can neither understand nor comprehend the fears of the fans," he said. "I have been asked to restructure the club, over a year ago Schalke was in a crisis. If you no longer want that, than I'm the wrong man.”
Schalke open their Bundesliga season against Hamburg on Saturday night.