Smith has signed a two-year deal at Elland Road after seeing out his contract at Oldham earlier this summer.
McDermott is working on a number of other deals and is hopeful of being able to name his second new face in the near future.
"We are still talking and getting closer to a few other deals. I am very close to another one," McDermott told the Yorkshire Evening Post.
"We are getting close to verbally agreeing another deal and are inches away. My view is that once I have verbally agreed a deal, it's a deal.
"If the person decides that they want to sign somewhere else after they have verbally agreed a deal, then they can go. Because you would not want that person anyway.
"For me, a verbal deal and a shake of hands and it's done.
"Hopefully, we will get the deals done as quick as we can. (But) if we can't get them done until July, we will wait until July."
Leeds have been strongly linked with a move for former Reading striker Noel Hunt who is available on a free transfer.