The Mosque Studies Center - Cr Doyle said Melbourne was one of the great multicultural cities of the world and agreed there was a need for a bigger site.
"I think a mosque would be a wonderful addition to multicultural Melbourne," he said.
Lord Mayor Robert Doyle says a mosque would be a 'wonderful addition to multicultural Melbourne'.
"We have a wonderful Islamic community in Melbourne and as far as I'm concerned, they are most welcome in the centre of our city."
He was responding to comments from the Islamic Council of Victoria that it wants to create a mosque for more than 2000 worshippers either in the Hoddle Street grid or Docklands.
Demand for space at the council's existing inner-city mosque, in Jeffcott Street, is so great that a garage has been tuned into a temporary prayer room.
Muslim community celebrates the end of Ramadan at the City Mosque. Photo: Neil Newitt
The council's president, Byram Aktepe, told ABC radio on Friday that the current city mosque was built for 300 people but now makes room for 2000 people over two daily services, across three floors.
"We're looking at a mosque that could cater for more than that," Mr Aktepe said.
He said that a central location to ensure that it is easily accessible was important. He said the council would be open to using a historic building.
"[We'd like] something that's appealing to the eye and something that blends in with the local fabric," he said.
"If it's a standalone building, we'd like something to be uniquely Australian in how it looks — not a traditional type of mosque with lots of minarets and that sort of thing."
Cr Doyle said he liked the idea of a traditional site being used.
"They will need a planning permit but we're happy to work with them should they find an ideal building," he said.
Cr Doyle dismissed speculation that a large mosque would be a security concern, saying many Jewish temples and schools dealt with safety issues appropriately.
Recent proposals for mosques across Victoria have been met with strong opposition and violent public rallies.
There was a long-running dispute about the proposed mosque in Bendigo, plus angry scenes that met proposals for mosque in Melton and Narre Warren North.
"I hope we wouldn't see that sort of behaviour," he said of such anti-Muslim protests.
"I think it's very un-Australian."
Mr Aktepe anticipated the new mosque would be funded by the local Islamic community and that the building would cope with population growth over the next 40 years.
It would also include an education centre.
"We don't want to be spilling out to the streets. That's the problem that we face if we don't address it in the next few years," he said.