Is it OK to ask not to contact current employer?
It’s perfectly acceptable to answer no to contacting your current employer. Most employers understand this and usually won’t have any effect on their decision. Make sure you have a back up of other references or employers they can contact. It’s usually okay to answer no for can we contact your current employer.
Do you mention current employer in cover letter?
Don’t shy away from the fact that you’re currently employed while searching for better opportunities. Your cover letter can highlight your current role and responsibilities, and you can use it to explain why you’re in the market for a new position. Example: I am currently a department manager at Wave Water Company.
Can your current employer be contacted?
Prospective employers usually understand the nature of a confidential job search and will not contact your current employer unless given permission to do so. Still, it’s a good idea to let anyone know your current employer is unaware of your job search and ask that they respect your privacy.