The council wants to save £44,300 from the museums service budget during the financial year 2013/14 and cuts to opening hours are one of the options being considered.
The gallery which has about 6,500 visitors a year, could be closed Monday to Wednesday and its hours reduced by two per day, according to a report to the council. The second option is to maintain the existing opening days but reduce them by three hours per day.
The report says: “With the Smith Art Gallery it is proposed that we work with local people to develop a volunteering model to help maintain and potentially increase opening hours over the next two to three years.”
Coun Pauline Nash, spokeswoman for communities, said: “This is a restructure of the service and it will affect staff contracts, jobs and put some at risk of redeployment or redundancy.
“We will hold a 90-day consultation with staff affected and hold a public consultation to get views on opening times and other proposals.
“The proposals we have put forward mean that we will continue to provide a local musems and galleries service which promotes our heritage.”
The proposals will be put out to public consultation.
Tom Ratcliffe, chairman of the Friends of the Rydings, said: “I am very disppointed that we are again talking about cuts to the opening hours.
“As a group we are against these proposals and will be making a response. The trouble is that the more opening hours are cut, the harder it becomes for people to visit. It’s a vicious circle.”