York manager Gary Mills told BBC Radio York: "Luton have shown interest and David wants to speak to them with regards to going.
"That's not going to happen unless we say it is. He's contracted until 2012 and I'm doing all I can to keep him."
McGurk joined the Minstermen from Darlington, initially on loan, in September 2004.
"It's part and parcel of football," added Mills. "I have to make decisions with players on and off the field. Players have to make decisions themselves and David's made that decision.
"Certainly looking at my squad of players and looking at David, he's somebody I wanted to have around and progress with to the extent that I've offered him a new contract again, which he's declined.
"He's somebody I don't want to lose, he's a good player."
Midfielder Alex Lawless has already left the Minstermen for Luton this season in a loan deal that will become permanent in January.
Source: BBC Sport