The Sky Blue Trust is urging fans not to buy shirts or merchandise until it is confirmed the team will play its home games at the stadium next season.
It said although the team had been offered the chance to play there "rent-free" the situation was still unclear.
Administrators confirmed on Friday the League One club had been sold to the Otium Entertainment Group.
Otium is owned by Sisu, the company that currently operates the club.
Trust spokesman Moz Baker said: "The clock's ticking all the time. There are no season tickets being sold - people need to know where we're playing and that should be in Coventry.
"We have a perfectly good, purpose-built stadium here which we should be playing at."
The trust also erected a makeshift statue to Joy Seppala, who is the head of Sisu.
Mr Baker said: "That idea was based on [chief executive] Tim Fisher's recent suggestion that there should be a statue of Joy Seppala outside the ground because of the £45m she has put into the club.
"It was just a light-hearted look at the situation which people are very upset about."