Yes, and there are two ways to do it that produce very different outcomes. Selling your membership interests transfers the company entire, with its contracts, licenses and liabilities. Selling the assets leaves the company with you and moves only what is listed. Which one happens is negotiated, and the operating agreement may have a view.
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How to sell your LLC: interests or assets
A membership interest sale keeps contracts, licenses and employer registrations in place, which is convenient, and carries the history, which buyers dislike. An asset sale gives the buyer a clean start and a fresh tax basis, and leaves you with the entity to wind up. Buyers usually prefer assets; the gap is settled with price.
What the operating agreement controls
Transfer restrictions, rights of first refusal for other members, consent thresholds and whether a majority can compel a minority to sell. Read it before you spend money on a process. A member who can block a transfer is a negotiation to have early rather than during exclusivity.
What a buyer will check
That the membership register and any capital accounts are accurate, that loans between members and the company are documented or settled, that the company is in good standing in every state where it trades, and that contracts do not terminate on a change of control. Each is easy to fix early and awkward to fix late.
Other questions people ask
Can a single member LLC be sold?
Yes, either by selling the membership interest or by selling the assets. The choice mostly affects tax and which liabilities travel.
Do other members have to agree?
That depends on the operating agreement, which commonly restricts transfers and gives other members rights of first refusal.
Which is better for tax?
It depends on your basis and the allocation of the price across assets. This is a question for your accountant before the structure is agreed.