  The near horizon geometries are usually constructed by implementing a
specific limit to a given extreme black hole configuration. Their salient
feature is that the isometry group includes the conformal subgroup SO(2,1). In
this work, we turn the logic around and use the conformal invariants for
constructing Ricci-flat metrics in d=4 and d=5 where the vacuum Einstein
equations reduce to a coupled set of ordinary differential equations. In four
dimensions the analysis can be carried out in full generality and the resulting
metric describes the d=4 near horizon Kerr-NUT black hole. In five dimensions
we choose a specific ansatz whose structure is similar to the d=5 near horizon
Myers-Perry black hole. A Ricci-flat metric involving five arbitrary parameters
is constructed. A particular member of this family, which is characterized by
three parameters, seems to be a natural candidate to describe the d=5 near
horizon Myers-Perry black hole with a NUT charge.
