Full Idea
Menzel proposes that an ordinal is something isomorphic well-ordered sets have in common, so while an ordinal can be represented as a set, it is not itself a set, but a 'property' of well-ordered sets.
Gist of Idea
Maybe an ordinal is a property of isomorphic well-ordered sets, and not itself a set
Source
Ian Rumfitt (The Boundary Stones of Thought [2015], 9.2)
Book Reference
Rumfitt,Ian: 'The Boundary Stones of Thought' [OUP 2015], p.275
A Reaction
[C.Menzel 1986] This is one of many manoeuvres available if you want to distance mathematics from set theory.