Can you ask a prospective new company not to call your old company as a reference ? And if you do, would that raise a red flag ?

It sure would raise a few questions, in fact many. It would bring the whole thing under more scrutiny.

IF you are currently working, you can ask, that they not contact them, till after you leave. But then if there is a issue, you could be let go by new company.

As someone that did a lot of hiring, if someone asked for a reference not to be contacted, we would ask them why, and expect a very good reason. Even then, it may put a "bad light" on that person.

Is this your current employer or a previous employer. There should be no problem asking that your current employer not be contacted, but it would raise flags to ask that a previous employer not be contacted.

I agree with Scott. It is not at all uncommon, nor does it raise red flags, to ask a prospective employer to contact a current employer. You could risk losing your current job should they find out you are seeking alternate employment b