The Shrews have so far brought in four new faces over the close season, with Alex McQuade, Dave Winfield and Tamika Mkandawire arriving on permanent deals and Akwasi Asante coming in on loan from Birmingham.
Town need to strengthen further as they look to again survive in League One next term but Turner insists he will not rush into any potential deals.
"I could sign a couple of players tomorrow and then regret it in a month's time," he told the club's official website. "I think it's worth waiting for the right ones and working towards the quality that we need to establish ourselves as a League One club.
"There's stacks of players out there. Would anybody feel easier if I went out and signed a couple that proved not to be good enough in the long run?
"I think most clubs are cutting down on the size of their squads. We'll be no different so you've got to be very selective.
"The first thing we check on now is character. We've got to make sure that anybody we bring into the club is of the right character as well as having the right ability.
"That selection process will go on."