Reports on Tuesday claimed the striker would seek a recall in order to join a top-flight side for the rest of the campaign, with most of the division's struggling teams interested in taking him.
"Tammy has shown no inclination to go back to Chelsea," Smith said. "In the conversations I've had with him he is enjoying himself at Villa and is developing as a player.
"He is very happy and you can see the connection he has with the supporters, the players and staff. We are very happy with the way Tammy is developing as a player and as a person.
"Chelsea seem very happy, as he is developing as a player and scoring goals in the Championship. For all three parties it is win, win. So I would be amazed if anything happened to prevent him playing for Villa.
"But it is not in my control. If Chelsea decide to recall him - it is up to them."