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When interviewing for a position, one of the 1st questions asked is whethre you are currently working, do you mind if we contact your current employer for references, etc.

The question of when you can start should also be addressed. That is the time to justity your desire to provide notice to current employer. If they suggest that they need you to start sooner than that, how can they hold that against you?

All you need to do is explain that I need to inform my present employer first, I'll get back to you if there is any difficulty in giving less than customary notice. Any employer worth his title will not hold you back from a seek a better job. At best, he may ask if you could work on a weekend to come in and clean up left over work.

the key is to negotiate start date as well as how soon you can leave the old job. Done correctly, you can leave on a professional note, even though the former employer is not joyous, he can at least know that you sought his approval - same with the new company.