The 23-year-old midfielder is set to leave Sheffield United this summer after Blades boss Neil Warnock released him last week.
Burnley and Stoke are also keen as his agent Lee Payne told skysports.com: "We are aware of the interest from those three clubs. There is a lot of interested clubs.
"Neil Warnock is willing to let Nick leave, but not for free and so some sort of fee will be involved."
Ironically, Montgomery used to be on the books at Elland Road.