You can take on and apply for as many international jobs as you want, and your club wont care. You just can't be seen applying to other nations when you already have an international job and other clubs when you have a club job.
Eg. You are Manager of Chelsea and you see that the Russia Job is available, you can apply for it. The club won't mind.
You then take the Russia job and also manage Chelsea.
You then apply for the Man United Job, and Chelsea would most likely fire you. But you can continue to keep the Russia Job.
But if you then apply for National Manager of England, Russia might fire you!