他說，重新命名市政廳廣場將是一個 "很好的起點"，通過捐款為廣場建造一座已故君主的雕像，將是一個 "恰當的紀念"。
負責經濟發展的內閣成員薩拉-博格爾說，工黨政府 "廣泛支持 "向女王致敬的想法。
The council agreed to set up a cross-party working group to decide on tributes to the Queen.
It will also decide on events in the city to celebrate the forthcoming coronation of King Charles.
Speaking at a meeting of the council on Tuesday, Mr Fuller said the Queen had "provided leadership and stability in uncertain and challenging times".
"It is right and proper that we as a city take measures to properly recognise her reign and service," he added.
He said renaming Guildhall Square would be an "excellent starting point" and a statue of the late monarch for the square, funded through donations, would be a "fitting tribute".
Cabinet member for economic development Sarah Bogel said the Labour administration "broadly supported" the idea of a tribute to the Queen.
"It's worth keeping an open mind - it's got to be about what the public want and what makes sense. There are lots of ways of to commemorate," she added.
"This will include, but not limited, to looking at the renaming of Guildhall Square, and the commissioning of a statue of Her late Majesty, funded through public subscription and donations, as a starting point for discussions," it said.