Grandma’s basis is as of the date she acquired it, minus depreciation, via the deed conveying it to her from the estate. The long term capital gain rate is 15%, so she would only be paying little taxes. WHY does she want to sell it now? How many heirs besides you? If multiple heirs do you expect there to be any family conflict over what to do with the house, versus splitting the money equally?
Conveying the property DURING HER LIFE, triggers the taxable event, “gifting” it to you does the same, on the amount over the annual gift exclusion.
If grandma is really elderly, some of them are pretty young, and thinks she’s only got a few years left, the best thing to do (to avoid cap gains taxes) is to have the ppty disposed of THROUGH HER WILL. That way when you (and whoever else) acquire it you will receive the “stepped up basis”. You could sell it the next day for NO GAIN and therefor NO TAXES. This also gives her the benefit of having the rental income for the rest of her life
Sounds like you are saying she inherited the property. If she inherited it, her basis would be the fair market value on the date of death of the previous owner, decreased by depreciation, increased by improvements.
The rule on stepping up the basis at time of death may change if the estate tax is repealed. If repealed, the step up in basis may go with it and you would, most likely inherit it at your grandmother’s basis.