The young centre back has at last begun to establish himself in the first team but is out of contract in the summer and is unhappy about the new 12-month deal offered to him.
He told nufc.co.uk: "The ball is really in the club's court now because I have rejected the offer they made me and I'm waiting to see if they come back with another offer for me.
"I'll just have to wait and see what happens, but hopefully things will be sorted out one way or another by the start of next month."
However Sir Bobby has reiterated that the club has made its final offer and it now looks likely that his younger brother Gary, who has recently completed a season-long loan with Coventry City, will replace Caldwell in the first team squad next season.