Wilson was forced off with a thigh injury during the 2-2 draw against Southampton before the international break and also missed Newcastle’s 4-1 defeat to Manchester United last weekend.
The 29-year-old has scored twice in the Premier League this season but Newcastle have yet to pick up their first win of the campaign.
“His recovery is going as well as it can. These things are about time and, unfortunately, Friday comes too quick for him,” Bruce said.
The Newcastle boss confirmed that Joe Willock, Javier Manquillo and Ciaran Clarke are fit to face Leeds after picking up knocks in the closing stages of their defeat at Old Trafford. Ryan Fraser has also returned to training and is in contention to play.
Newcastle host a Leeds side who are also looking for their first win of the campaign and Bruce was forced to defend his position at St James’ Park ahead of the match.
“It’s not all about me,” he said. “I’m here to only do what I think is best for the club and that is managing it as best I can and keep us moving along.
“I will continue to do my best. I’m never going to walk away from the challenge.
“It’s always difficult. The frustration is, like any other Premier League club, if you don’t get results then ultimately the manager, head coach, whatever I am, bears the brunt.
“I have to accept that results haven’t been good enough. The disappointment was we played very well at a difficult place last week - as difficult as it was going to get. We played very well and didn’t get anything out of the game, which was the frustration.
“We’ve had some awful decisions with VAR and penalties and all the rest of it. How quickly it spirals downwards here but I’ve witnessed the other side.
“A win can do wonders and hopefully gets us started. Hopefully we can build a little bit of momentum because we proved at the back end of the season with momentum behind a club like ours, it can only be a good thing.”
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