Mr Bates said he and his wife Suzannah offered to personally pay the estimated £1.25m cost of setting up a United museum in Elland Road’s East Stand following Leeds’s takeover in 2012 by Dubai-based investment bank GFH Capital.
Profits from the museum would have gone to the Leeds United Foundation, the club’s charitable arm.
Mr Bates claims, however, that his offer – made in the spring of 2013 – was never even acknowledged by GFH.
He was speaking following the revelation that the area in the East Stand previously earmarked for a museum has been rented out to a law firm.
Mr Bates said he could understand the decision by the club’s current owner Massimo Cellino to rent out the space to try to maximise week-round revenue.
But the former Chelsea supremo also described the absence of a museum at Elland Road as a “missed opportunity”.
He said: “The situation is not as good as it could have been. Leeds have got a fantastic history and it needs to be told.”
A United museum was talked up as a permanent new attraction at Elland Road while the East Stand was being redeveloped during Mr Bates’ tenure as chairman.
But last week it emerged that around 85 workers from a firm called Quindell Legal Services Ltd are now using the space it would have occupied on the East Stand’s first floor.
Mr Bates took charge at Leeds in 2005 but stood down as chairman after GFH’s purchase of the club.
He was due to stay on as president at Elland Road for a further three years but parted ways with United in the summer of 2013.
Italian businessman Mr Cellino bought a 75 per cent stake in Leeds in February 2014.