Mayor-elect Rahm Emanuel has reiterated during his campaign that he won't retain Weis, saying the morale battle between the city's top cop and the police department is too expensive.
Weis has come under fire in the past for not having enough officers on the street.
Retiring Mayor Daley, though, continues to stand by the man he dispatched from the FBI to take over the department in 2008 following Philip Cline.
Daley said during a gun laws press conference on Monday that he won't ask Weis to leave and "hopes he stays" until May.
Will Weis want to stay?
If not as superintendent, then at least in Chicago.
During an unrelated press conference Sunday, Weis told reporters he'd wait and see, and that he'd look into another position in Chicago when this one ends.