The Owls have raised expectation levels for the 2015/16 campaign after going through their last seven matches in all competitions unbeaten.
Wednesday have beaten Newcastle United in the Capital One Cup, while they have moved into the top half of the Championship table as a result of their fine form.
And Turner said: "The way we are playing at the moment, the way we are digging in for each other and getting results, there is no reason why we can't be in the top six.
"But, it's a tough league. It's really tough this year, and we have to take each game as it comes. Hopefully we'll find ourselves in a position towards the end [of the season] when we can have a really good go."
Turner was one of Wednesday's new arrivals during the summer transfer window, and he has immediately made an impression at the club.
The Norwich City loanee has come straight into the Owls' defence, and he is yet to taste defeat during his time with the Yorkshire outfit.
Unfortunately for Turner, he is out in injured at the moment, and he will miss Carlos Carvalhal's side's match against Rotherham United on Friday evening.
If Wednesday can win that fixture against their local rivals, they will move to within just one point of the play-offs, putting them in a good position to achieve Turner's aim.