Yes, you can sell a business with an SBA loan, but not without taking certain important measures. The most crucial measure is obtaining lender approval.Assumption of Loan Requirement Letter for disaster loan servicing action request packages. About this document and download. Can An SBA 504 Loan Be Assumed? Many types of loans are not assumable. In this article, we will discuss pros, cons, who qualifies, and how to fill out SBA Form 413 to get an SBA loan. Fortunately for borrowers, SBA loans, including the SBA 7(a) loan, are fully assumable with SBA approval. Under what authority? The SBA doesn't assume loans.