But Irvine, who has already had to sell goalkeeper Lee Grant to Burnley to help pay off the club's debt to HMRC, is adamant the 27-year-old will not be sold on the cheap.
Talking to the Sheffield Star, he said: "A club did show an interest (in Tudgay). They were well short of anything that would tempt us.
"I think everyone is looking at the Lee Grant situation and thinking that Wednesday are a selling club now. We're not.
"We're not in a position where we have to sell. It was a Premier League club who made an enquiry (about Tudgay) but they didn't make a Premier League club's offer."