Is there a C# equivalent to Delphi's assignable const?

In Delphi you can declare a constant in a method and assign it a value in that same method. The idea is that next time you are in this method, the const will still have the same value that you last assigned it.

It looks like this in Delphi :
(I don't have Delphi here so it is untested, sorry about that, but it is enough to demonstrate what I mean)

procedure Form1.test;
const
  AssignableConst: Integer = 0;
begin
  ShowMessage(AssignableConst);
  inc(AssignableConst);
end;

Every time you call the procedure test the messagebox will show the last value + 1

This example is completely useless I know that it is just to show how an assignable const works in Delphi.

Is there an equivalent for this in c# ?
I don't want a solution that involves private variables in the class, it has to stay inside the method.

My question is about scope. Nothing else. I don't care that the value is part of the state of the object. That is not important. What is important is that I need a variable that is only accessible from the scope of a method, nowhere else.
In Delphi this can be done by using an assignable const, so how can I do this in C#?