The politicians met yesterday to discuss the way forward and agreed that a public meeting in June was the best option.
Coun Green said: “It was a good and positive meeting. I will write to Sainsbury’s and so will Philip Davies, to invite them to talk about their plans for the building.
“It came from people contacting me and Philip on Twitter asking what was going on.”
He added: “It is the future of the Bradford & Bingley building that is key.”
Sainsbury’s, which owns the building in Main Street, is proposing to open a smaller store in Main Street.
Coun Green said he and Mr Davies also discussed developing a plan for Bingley, including issues such as the swimming pool and the market.