OPENROWSET

what you can do is - you can execute a stored procedure in a query using OPENROWSET option and can change your query as,

select top 3 newsid from staff s,
OPENROWSET('SQLOLEDB','Server=(local);TRUSTED_CONNECTION=YES;','set fmtonly off exec master.dbo.spu_SdOtherNews')
AS a
where
s.id <> a.id
order s.id desc

Assuming spu_SdOtherNews is in Master databawse and it returns the list of ids.