The 27-year-old is a target for a number of clubs in the Championship, with Stoke City, Fulham and Birmingham City all joining the list of possible suitors.
However, the League One side are not keen on losing him after an individually successful campaign where he managed to score ten goals in 44 matches.
Millwall’s previous offer was £400,000 which was to be paid over the course of a number of instalments.
Now Millwall are claimed to have offered around £1m for Windass, which Sheffield Wednesday have also turned down.
Windass has a year left on his current contract with the Owls, who have the option of extending the deal by one more year.
Millwall finished eleventh in the Championship last season, 15 points off a playoff spot.
It remains to be seen if they will make another move to try to convince Sheffield Wednesday to sell Windass.
