Suppose that you are invited by another company to attend an interview which you do not want your current employer know about it. You have to apply visit visa in order to attend the interview because it is not in your residential country. To apply visa, you need a proof of employment from your current employer and proof that you're given time off on the date of intended arrival. The problem is most likely your current employer will ask you the purpose of visa application. What should you say? Vacation? If you can advise me sample of the letter, that will be helpful.
Since you don't have the job yet, you can't be applying to a work visa yet. So you will be applying to a tourist/business visa, which should not raise any alarm bells on your company. You just want a visa to travel to that country and it is no one's business where you spend you vacation time.
So the purpose of your VISA should the employer ask is, truthfully, tourism (for now).
To apply visa, you need a proof of employment from your current employer and proof that you're given time off on the date of intended arrival.
Frankly, I have troubles understanding that. And what if you didn't have a job and were invited for this face to face interview? You couldn't go?
I'm just saying this to make sure that you understand the difference between a tourist and a business visa (the latter being something very different from a work visa).
Per my understanding, your prospective employer is giving you an official invitation and is covering the cost of the visit. Since he is able to do that, we're speaking most likely about a larger company and important tax payer of this country. I can't quite imagine that you would need anything else in addition to that to get a visa from this country's consulate.
If they insist on a proof of employment, you might just provide your latest salary statements. If your company is larger, it might have a separate HR department where you can request such proof without your line manager knowing. As a last resort, you could make up some story that you need the proof for some kind of purchase, or renting a new flat, or whatever makes sense in your country.
The biggest issue is the "proof they have given you time off". Again the question, are you sure that's a requirement for a business visa? Sure, you could lie about going on vacation, but in my country the employer has the right to decline this request while he could not decline me going to an interview. So, this really depends on your local rules.
I would strongly urge you to speak to someone in the consulate in person (not just the visa desk front staff). Explain them your case and see what they would really need, and if they could provide a certain amount of flexibility considering documentation needed from your current employer.