The 29-year-old has three goals and one assist against the Whites to date in his career, including a controversial winner for his previous club Queens Park Rangers.
Wells' 20th-minute winner at the Kiyan Prince Foundation Stadium came about after Eberechi Eze's free kick made contact with both of the forward's arms before he tapped into the net.
The Bermuda international is now gearing up to face Marcelo Bielsa's side for a third time this campaign.
In the January transfer window, Wells was recalled from his QPR loan spell by parent club Burnley before being sold to the Robins in a deal worth around £5million (BBC Sport).
"With QPR we lost 2-0 [at Elland Road], it was a very dominant performance from them," he told the Bristol Post. "It was a tough game, probably the toughest I've featured in this season - all credit to them, they were good.
"I got the better of them at QPR at home, I got the winner, so I'm familiar with scoring against them. So I do have a history with them and it's one I'm looking forward to. It's a fantastic stadium, a well supported club and one moving in the right direction. But we're here to stop that."
Wells scored his first goal for Lee Johnson's men in the midweek 3-2 victory over Derby County at Ashton Gate.
City are currently seventh in the Championship table, level on 53 points with sixth-placed Preston North End, while Leeds are second in the standings, level with third-placed Fulham on 56 points.
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