The Royals asked about the 21-year-old striker's availability when Yann Kermorgant was sidelined with a serious hip and groin injury.
The move never materialised, however, and Stam bolstered his strikeforce by landing Jon Dadi Bodvarsson from Wolverhampton Wanderers for around £1m.
Wilson has now re-emerged as a target for Reading and, addressing the rumours, Stam told a press conference: "I know about it and we already spoke about him in June. But at the moment there is nothing in that.
"I'm not going to name names, but we are looking at players. We're looking at the team, how we are set up and asking whether we need to do anything and bring in players in certain areas.
"So yes, we are looking at certain players who can improve the team and add extra quality to the squad. But that's not going to be easy because clubs don't want to sell their best players in January."
Wilson has not made a Premier League appearance for Man United since October 2015.