Do concurrent: can loop variable be specified in `local`?

This is a numbered constraint meaning that a standard-conforming Fortran processor (i.e. compiler) should be able to diagnose it (J3/24-007, page 32, paragraph 2):

A Fortran processor shall:
[…]
(3) contain the capability to detect and report the use within a submitted program unit of a form or relationship that is not permitted by the numbered syntax rules or constraints, […]

The line you’ve shown violates the constraint:

do concurrent (j = 1:Ny) default (none) shared(image) local(i, j, x, y, x_0, y_0, x_sqr, y_sqr, n)
!              ^                                               ^
!              index-name                                      variable name in locality spec