Thank you for your response. The Owner didn't put his initials or a name, but he did include a confidentiality notice on the bottom of each of his emails. The Property Manager either put her name or a full signature on her emails. I discussed signing an extension for one year with the Owner. He agreed and told me to contact the Property Manager. I contacted the Property Manager and she replied asking the exact date I wanted the new lease to end. I told her one year from when the current lease ended and she sent me an email response saying that was okay.
At this point, whether you agreed to an extension or only agreed that you would later sign an extension agreement is not clear. A lawyer would have to look at the emails themselves. Even then, whether you intended your emails to be legally binding would be ambiguous.