We bought a nail salon business in December 2019, but never claimed the purchase price as part of the K1 basis for our S-corp income. In 2020, we sold our rental property at a loss from the original purchase price plus capital improvements, so I would like to defer claiming the purchase price until this year - 2021 - as I expect our income to be significantly higher now that the Covid-19 crisis is winding down. Is that permissible under the tax laws?
At this point, you most likely will need to consult with a tax professional (link below) and legal counsel.
At both the point of purchase and sale, a Form 8549 probably should have been filed.
See https://www.irs.gov/instructions/i8594#idm140044360310576
Regardless, there is no option to "defer claiming the purchase price until this year".
That's exactly what I did when I filed our 2019 taxes - consult a professional. She told me that it wasn't necessary as we had a loss anyway (all the expenses such as buying previous owner's inventory/supplies, legal and other fees, etc). She also said that when we sell the business, we could deduct the purchase price from the sales price at that time.
It is not entirely clear exactly what you purchased, but if the purchase involved assets to which goodwill or going concern value attached, or could attach, and if the basis in the assets is determined only by the amount paid for the assets, then an 8594 was required to be filed.