Jon Taylor, Aaron Wildig, Connor Goldson, Jermaine Grandison, Tom Bradshaw and Ryan Woods are all out of contract this summer but were presented with fresh terms at the end of April.
They have exactly one month - until May 29 - to respond to Town and either accept or reject the contract offer, although Turner, who has seen young winger Jack Gwilliams pen his first professional deal, has not received any indication of their decisions.
"I've heard nothing at all from any of them," the Shrews boss told the club's official website. "Young Jack Gwilliams has signed a contract but the rest of the Under-24s that are out of contract that we've made offers to, I've not heard anything yet.
"It doesn't surprise me as some of them have gone away on holiday, others will leave it right until near the deadline. They have to inform us by May 29 whether they accept our offer or not.
"I would expect there should be some discussions before that date but that remains to be seen."
Turner wasted little time snapping up defender Alex McQuade, 20, following his release from Bolton and admits he has held talks with other transfer targets.
"I've met with a couple of players just to talk about football, kept their agents out of the way as I didn't want to talk about contracts," he added. "It's to get to know them and see if there's any rapport.
"I've done this over quite a number of years. I just like to sit there and talk to them about football for an hour and find out their views, find out what motivates them, and all the rest of it.
"The two players I've spoken to so far I've been impressed with and we might make offers before the end of the week."