A potential client wants me to look at his bookkeeping with QuickBooks online. Is there a way to download the information to use with my QuickBooks desktop?

Which QB Desktop year version do you have? You can convert data to QB Desktop. Then you convert it again to a new (trial) QBO account.

Thank you for posting to the Community and letting us know about your concern in managing clients' books in QuickBooks Desktop (QBDT), @DreamaM3. 

Since QBDT and QuickBooks Online (QBO) are two different accounting systems, there are differences in managing each client's books. Therefore, we're unable to download your client's bookkeeping records from QBO to review and make changes. 

Moreover, you can opt to create a QuickBooks Online Accountant file to connect to your client's accounts, review their books, edit transactions, and fix issues. You can head over to this website to sign up for free: QuickBooks Online Accountant.

After that, you can ask your client to invite you as their company accountant. Please refer to this article for complete guidelines: Add accountant users in QuickBooks Online.

Let me know if you have more questions about QuickBooks-related concerns. I'm always here to help, take care!