Tenants doesn't want to sign

[Jose Sarabia]

Please help! I just bought a tri plex, and one of the tenants older (mean) guy, says he's moving out so he doesn't want to sign a new lease, but he doesn't know when,(he said idk when in two or three months he said)  and shut the door on my face when I went to see him about letting me  know when hes moving out, so stress about dealing with him already what do I do? And I don't even know if he will pay for the next and two months that he will live there , should I just give a writing letter that I give him till the end of May to move out because he doesn't want to sign a lease, please help!? And how should I give him the letter because he won't open the door anymore, Thank you  for taking the time to read this!