Striker Collins was top scorer for the League One new boys last season, but decided to join fellow promotion winners Swindon after rejecting a new contract at the Greenhouse Meadow and because the player is under the age of 24 Shrewsbury are entitled to compensation.
"We've started talking about a fee, but we've had no correspondence from them other than me chasing it up earlier this week," Turner told the club's official website.
"We're awaiting an offer, what we're looking for, and I would think the chances of it finishing up at a tribunal are quite high."
"We Obviously value James as a young player with stacks of potential. He's already a proven goalscorer at league level so we'll wait and see what Swindon's reactions are to the situation."