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Is it a red flag to employers when an applicant doesn’t want them to contact their current employer?

Basically I don’t want my current employer to know that I am looking around yet. However, this is the best job I’ve had so far in my field, so I definitely do want to include it on my application/resume. Would it hurt my chances of being hired even slightly if I checked NO for “may we contact this employer?” I’m admittedly a little underqualified for this new job I’m applying for, so I really need all the help I can get.