Paterson, 21, is regarded as one of the best talents in the lower leagues, leading to speculation that a number of clubs were preparing a January move.
However, Smith told the Express and Star: "I have seen the reports. We've had no contact at all from Sheffield United. It's that time of year and there's rumours going around all the time.
"I can't really comment because we haven't had anything from Sheffield United. Even so, I can't see why we would want to sell one of our promising young players to a team in our league."
Walsall currently sit 12th in the League One table.