A planning decision on the club's proposed new stadium at Ashton Vale is expected on November 4, while permission is being sought for plans to turn Ashton Gate into a Tesco supermarket the following day.
City chairman Lansdown told the club's official website: "We appreciate the efforts of those fans who have already signed various petitions and turned out at meetings to show their support.
"But time is now running short and those people who want the new stadium and think it's a good idea have to say so in the very near future if they want to be heard.
"We believe passionately that this scheme will benefit Bristol and that it has to happen if our football club is going to move on and progress to the next level.
"It's a once-in-a-lifetime opportunity but we need to win hearts and minds and the fans have a big part to play. I would ask all those, who have not yet pledged their support, to do so now and make their opinions known and their voices heard. By next month, it will be too late."