Tenant give move out notice, new tenant ready to move in, but current tenant changes mind. Now what?

I am a tenant in Wisconsin who rents out the other side of my duplex. The tenant has fulfilled their 1-year lease, and is now month to month. They gave me a 60-day move out notice. I then started showing the apartment and have a new tenant ready to sign the lease to move in. Now the current tenant is saying they might want to stay, even after giving their notice. Do I have to let them stay or can I make them move out?