I have a player who was willing to sign a contract last season, but I couldn't re-sign at that time because it would have put me over budget for the second year of his deal.

Now, after rollover, he states that he will go where the money is but did not outright say he would test the FA waters.
Is it possible to sign him to a deal before FA signing starts?

I'm hoping there is a certain % over his initial demands that would get this done.

1)  What they say before budgets are set is not accurate-- you will find out after budgets lock in what his real intentions are.
2)  Whatever he says after budgets lock in goes... he may very well take an offer at that time.

thanks.