Lions boss Neil Harris has made the 27-year-old, who scored 11 goals last season, his top summer transfer target as the relegated club prepare for life in League One.
Millwall chief executive Andy Ambler made the improved offer to Bantams chairman Mark Lawn when the pair met at a Football League conference in Portugal, but his latest bid was knocked back.
Lawn told the Telegraph & Argus: “I had a chat with him over there and he moved his bid slightly. But it’s nowhere near the valuation that we put on James.
“So unless they meet our criteria, James will remain our player.”