Forlongs' lawyers have challenged the road being open for 51 half-days a year because they are only half-days.
Hamilton City Council city infrastructure general manager Chris Allen said an agreement had not yet been reached between the parties, despite several council-led mediation meetings.
"These discussions will continue, however, with a report being brought to council next week to start a process to get public input into the various options. Council would only be asked to make a decision once this public input is available."
Forlongs' owner, Terry Forlong, welcomed the move to close the road on Saturdays, but said it would not solve the problem of there not being enough parks on the street if the market spilled into them. Mr Forlong has concerns about parking, security and accessibility to the shops when the markets are running.
"We are happy with the road and we would like the car parks open as well, because there's not enough car parking on Saturday morning without those.
"It would be like it is now, and we are trying to get more car parks for our customers and better access."
Frankton Business Association chairwoman Edwyna Carlson confirmed the group had put some options forward.
Frankton's smaller retailers have been fighting for the 20-year-old markets to stay open on a Saturday because the event brought in 2000 shoppers, and many stallholders and visitors already had Sunday commitments.