Hole in upper right molar -- Does my tooth need to be removed? (photo)

A piece of my upper right rear molar fell out yesterday. My dentist told me that the only options were removal (and no replacement) or removal with an implant. My dentist was not able to find any sold tooth structure at the bottom of the tooth and said a crown would not work. I have attached a photo of what the tooth looks like now. I would appreciate any thoughts on whether the tooth is salvageable. Thank you.