You are right that an integer infinity is possible, and that none has been added to the Python standard. This is probably because math.inf supplants it in almost all cases (as Martijn stated in his comment).
In the meantime, I added an implementation of extended integers on PyPI:
In [0]: from numbers import Integral, Real
In [0]: from extended_int import int_inf, ExtendedIntegral, Infinite
In [0]: i = int_inf
In [4]: float(i)
Out[4]: inf
In [5]: print(i)
inf
In [6]: i ** i
Out[6]: inf
In [7]: i
Out[7]: inf
In [9]: isinstance(i, Real)
Out[9]: True
In [10]: isinstance(i, Integral)
Out[10]: False
In [11]: isinstance(i, Infinite)
Out[11]: True
In [12]: isinstance(i, ExtendedIntegral)
Out[12]: True
In [13]: isinstance(2, ExtendedIntegral)
Out[13]: True
In [14]: isinstance(2, Infinite)
Out[14]: False