Michael Egan Iii reportedly wants the dismissal granted "without prejudice or an award of costs or fees, in the interest of justice", according to the New York Daily News.
He has already withdrawn cases against the other three defendants, Gary Goddard, David Neuman and Garth Ancier.
Egan is also fighting his lawyer Jeffrey Herman's motion to withdraw from the case.
The accuser originally claimed he had been abused at parties in Hawaii and Los Angeles from 1997 to 1999. when he was a teenager.
Singer previously filed a motion to dismiss the case with prejudice, which would not allow it to be refiled. That motion is scheduled to be heard on 9 September (14).