Red Dragons manager Denis Smith met with the 23-year-old front-man to discuss a three-year extension to his current deal which expires in the summer and indicated the star had upped his original demands.
"There seems to be some breakdown in communications because the figures Craig came back to me with and the ones I had discussed with his agent don't seem to match up," Smith informed the club's official website.
"We have made what I thought was a very good three-year offer to Craig and I thought we were near an agreement.
"It is a shame because we certainly can't afford to lose out on a player of his ability."
Wrexham now look set to sell Faulconbridge, currently sidelined with an ankle problem, to help balance the books at the Racecourse Ground.
"Every player at every club is for sale all the time. Unfortunately, it is something which can't be ruled out," added vice chairman David Rhodes.
