Is it illegal to buy stock options in a publicly traded corporation
and then make a tender offer for the corporation's stock at a premium
price per share and then sell the options once the tender offer is
public?

Probably. Thats big time conflict of interest. You simply cannot have
that some of insider information especially in public corporations but
any business really and that could be constituted as insider trading
becuase you have information that maybe no one or very few people have
and would most likely violate a lot of IRS rules.

please check with an accountant and a lawyer for a fully conclusive
and fully knowledgeable answer.