Magath is understood to be wanted by half of the club's board members to replace Van Marwijk and try to steer the club away from relegation.
The other half want to stick with the Dutchman and that is enough for Magath to pull himself out of the running.
"The board is against me," Magath said. "I've kept myself available for Hamburg all week.
"It would have been a perfect fit, for me and for the club."
Magath wrote on his Facebook page that there are "too many old heads who are stuck in their ways and not interested in an honest new beginning" whilst thanking fans for their show of support and inviting them to get behind the team "unreservedly" in their relegation battle.
That battle takes them to Eintracht Braunschweig on Saturday with Van Marwijk still at the controls in spite of a 5-0 defeat to Bayern Munich in the DFB-Pokal on Wednesday night.
"We've got to put Bayern behind us," said Van Marwijk, whose side have conceded three goals or more in their last six matches, scoring only twice in the 3-2 defeat to Mainz.
"This is the most important game of our season and we've got to be aware of that and be prepared for it."
It is also the biggest game of the season for Braunschweig, who could reduce the arrears on Hamburg to a single point with a win, but see themselves fall seven points adrift at the bottom with defeat.
"I still have the feeling that my team and club can deliver something in particular situations like this," said their coach Torsten Lieberknecht.