Given what you said above, here are some thoughts ...

Based on the assumption that you aren't taking over an operating business here (since you said there are no assets), but you still want to own the LLC, you'll need to purchase 100% of the membership interest from the current owners - it's considered a stock sale, as opposed to an asset sale where you would be buying the assets of the LLC from the LLC. The primary risk with a stock sale vs. an asset sale is that you are potentially acquiring all of the known and unknown past, pending, threatened and future liability the current owners may have. That's not to say you shouldn't pursue acquiring the LLC, it just means you have top make certain your attorney draws up a purchase agreement with all of the standard representations and warranties that indemnify you from these potential legal risks.

Another option would be to have them dissolve the LLC and then you can register it as a new entity. This could take anywhere from a couple of weeks to a couple of months to be completely resolved. But the bigger question with this strategy is to understand your motivation for wanting the LLC in the first place. If it's simply to own the name because there is some value in that in your marketplace, that's OK. But if it's because there are some customer contracts, vendor agreements or other contractual arrangements the LLC has that you want to have yourself, this strategy won't work - even though the LLC name doesn't change, the EIN will, and that will trigger the necessity for a new contract, agreement, etc., with the party you were hoping to seamlessly assume.