They’re likely open to hiring a freelancer on a project-by-project basis. Assuming they’re open to it, any longer-term contract work would probably come after you’ve proven yourself to them in their eyes.
How this is handled depends on the company.
I have several very long-term clients where we no longer bother with contracts. I have other ongoing client relationships where their preferred way of handling a contractual relationship is by issuing me a purchase order that lists a maximum dollar amount over a specific time. I have other occasional clients where every job is an individual contract — sometimes just an email (depends on how much I trust them.)
However, before you get to any of that, you need to sell them on the notion that what you have to offer is worth their investment. If they’re interested, study the company, figure out what they probably need, and figure out what you can do for them. Meet with the person who makes the decision, then play it by ear. Act confident and engaged in their business. Ask intelligent questions. Show them your work and discuss how it might relate to their needs. And probably most important, listen to what they’re saying and respond to them in ways that let them know that you get their concerns and understand their needs.
If the prospective client is interested, you or they will need to bring up the subject of money and conditions. Decide in advance what your bottom lines are. Decide how much money you want to make for whatever time you put into it.
Don’t get so caught up in wanting to nail down an agreement that you begin negotiating below your bottom lines. Always be prepared to walk away if the terms don’t suit what you decided on in advance. With me, probably three-quarters of the discussions end when I mention my terms. That’s not true for everyone, of course, but my point is you’re an equal player in any proposed relationship. They get what they need only if you get what you need and vice versa. A freelance job is not an employer-employee relationship. Instead, you’re an independent business person who has agreed to do work for them if they meet your terms. Always, always, always be prepared to walk away.
Keep in mind that freelancing comes with extra costs, so if you base your rate on how much you’d make per hour working as an employee, you lose money. As an employee, you might be OK with working for $XX per hour. You show up, you get paid for being there no matter what. As a freelancer, much of your time isn’t billable; you pay for everything that your employer would normally cover. In other words, you might need to charge twice what you would as an employee.