Monk, who has spent three months on loan at Hillsborough, is due to return to the Saints after this weekend's home game against Ipswich and Turner is in talks to keep the defender at Hillsborough permanently.
"I have really enjoyed my time at Sheffield Wednesday, it is a good club, and I have been grateful for the opportunity to play first-team football again," Monk told the Yorkshire Post.
"But until I have spoken to both clubs I can't say what is going to happen next."