You need to mark "no". You aren't eligible to work. Lying is not the way to begin your professional career.
The only work allowed on an F1 is on-campus employment*, which means working for the school, for a business contracted by the school (e.g. bookstore), or something educationally related to the school (e.g. research, work-study). Also, there are limits to the amount of work you can perform (20 hours per week maximum while school is in session, 40 hours during breaks), so check the proposed schedule. Does the job you're applying for meet these requirements? If so, you can mark yes. If you aren't 100% positive (and even if you are, it never hurts to double check), your school should have an office that can answer these questions for you. Go ask them.
If you mark yes on the application and you aren't authorized to work, the most likely outcome is that you're immediately rejected from the application process as soon as the company figures out that you don't really have the right to work in the US. The company is asking this question for a reason. You should be happy they're being up front about it, because you can realize that it's a deal breaker and not waste your time. "Oh, you aren't authorized to work here! So sorry, good luck, there's the door." - is this something you want to wait to hear after spending a few weeks interviewing and negotiating?
Most applications involve a statement affirming that everything you've said is true and correct, and the company reserves the right to reject or fire you if it turns out you lied. Lying about having the right to work is a huge deal, regardless of the reasons for doing so. Quite possibly word will get around about this (especially if you're going through recruiters), damaging your chances for employment once you are legally allowed to work.
Worst case scenario, you start working there and someone finds out your employment is illegal. They report you to the immigration authorities who come knocking on your door. Your visa gets revoked and you are summarily deported. This is not a position you want to be in. It's not worth the risk.
I fully expect to get OPT, I am intending to apply for OPT, but haven't done so yet.
Apply for it first. After being approved, you can mark yes for qualifying jobs. "Intending to apply" and "submitted an application" are far cries from "having authorization". Any company who decides to proceed with you under the assumption your application will get approved "later" will be very unhappy if it turns out you didn't get it after all, because they wasted a bunch of time and money on the hiring process. Even if you subsequently get authorization, such a company would very likely not want to consider you again after being burned.
*In cases of extreme financial hardship, you can get approved for off-campus employment, but you must apply for and be granted special written dispensation. I'm assuming this does not apply here.