The academy graduate has not featured since August 28, having fallen behind Keiren Westwood and Cameron Dawson in the battle for a starting spot.
But Wildsmith, an unused substitute in Saturday's thrilling 3-3 draw at Preston North End, could be given a run-out when the Owls welcome the R's to Hillsborough on Sunday.
Therer were eyebrows raised over Westwood's absence from the matchday squad at Deepdale. The experienced shot-stopper was left out, despite having recovered from the knee injury he sustained at Premier League-bound Norwich City, as manager Steve Bruce kept faith with Dawson in goal.
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Bruce told The Star: "I wanted to have a look at big Cammy. Maybe there is an opportunity next week to have a look at Joe Wildsmith too. We think a lot of Joe.
"I will make a decision next week on who will play."
The former Manchester United defender described their first half display against Preston as "awful". The Owls trailed 2-0 at half time thanks to a Jayden Stockley header and a Tom Lees own goal.
But Atdhe Nuhiu's introduction as a 67th-minute replacement for Tottenham Hotspur's loanee Josh Onomah lifted Wednesday. Nuhiu set up Fernando Forestieri for the Owls' second before getting on the scoresheet himself.
Defender Dominic Iorfa was shown a straight red card for a poor challenge on Preston full-back Darnell Fisher.
Bruce said: "There were a few words said at half-time and then in the second half we did the basics right and asked them a question. I thought our subs coming on gave us a bit of impetuous.
"I thought we still threw everything at them with ten men and we nearly could have won it at the end.
"I have to say the second half, for a neutral in awful conditions, was a great game and advert for the Championship.
"In the end, I have got to be pleased. I wish we had played like we did in the second half in the first and then we would have been worthy winners."