Rush took over at the Deva Stadium at the end of August, and has just ten games under his belt as a manager.
Yet the former Liverpool and Juventus forward now appears favourite to replace Mark Hughes as Wales boss.
Chester chairman Stephen Vaughan said: ''I don't know whether he has been offered the job but we are not going to stand in his way.
''He has done a tremendous job for Chester City but at the end of the day this is how it is.
''He has proved our decision (to appoint Rush) was right. Ian Rush is going to be a big name in football management.
''We would like to keep him but we can't compete with a job like the Wales job.''