The Shrews boss masterminded victories over Derby and Swansea in this competition last season while he was at the helm of Hereford when they knocked Leeds out of the FA Cup in 2007.
Turner is now eyeing another victory in Yorkshire, and he told Shrewsbury's official website: "Leeds will obviously be a tough encounter but I've got some good memories of Leeds. When we went there with Hereford in the FA Cup we beat them.
"I think we're quite capable of going up there and putting on a show and, if we do, you never know we might just get that little bit of luck which means we can be in the hat for the second round.
"I look through some of the first round draw and there's some clubs where the reaction to the Capital One Cup can be lukewarm, but I think with Leeds the supporters are so committed to the club that I'm sure we'll get a good gate there which will create a good atmosphere.
"It's certainly one to look forward to and we just hope we put on a show and maybe cause an upset."