No, but if you put that money into a bank account that earns interest then you'll report the interest income. If you stuff that money in your mattress, it's not earning anything, so you report nothing on your tax return. That money would have been reported on the estate tax return of the person that passed away.
If, instead of money/cash, you inherit stock or a rental real estate, then you still don't report the receipt of that property as income. It's only when the stock earns dividends or the rental real estate is producing rental income do you report the dividends and rental income on your tax return.
Then, obviously, when you sell the stock or rental real estate, you'll have income that needs be reported on your tax return. The income you report on that sale will be the difference between the money you received in the sale and fair market value of the stock or rental real estate on the date of death of your family member/friend. (For the sale of rental real estate, you'll also factor in depreciation.)