Liverpool council leader Warren Bradley has said he is confident Everton could still be kept in the city.
The council leader says a deal can still be done
Everton's chief executive Keith Wyness has said it was vital for the successful future of the club to move to a 50,000 capacity stadium in Kirkby.
A ballot is due to be held among the supporters - many of whom are concerned about the club moving out of Liverpool.
But Evertonian Mr Bradley has come up with four new sites which would mean it could stay in the city.
He said in a statement he had been working with the club, commercial partners and supporters to come up with alternative plans.
He said: "I am committed to ensuring that Everton Football Club has every opportunity to stay within the city.
"Everton does not have to leave the city, I am confident a deal can be done," he added.
Mr Bradley revealed two of the proposed sites are in the Liver Industrial Estate in Walton.
Another is on land near Scotland Road. A fourth is on the Axis site in Speke and the fifth is a redevelopment of the Goodison Park site.
The club fears their ageing stadium may struggle to get a safety certificate in coming years.
An artist's impression of the proposed stadium in Kirkby, Knowsley, which would cost £150m and could be ready for 2010, were released on Friday.
Financing of the stadium will be helped by £50m from supermarket giant Tesco.
Any cash Everton needed to put into project will be offset by naming rights to the new stadium and the sale of Goodison Park, which could raise about £15m.
Keep Everton in Our City campaigners and the Kirkby Residents Action Group have been protesting about plans to move to Kirkby.
Keith Wyness has said the results of the fans' ballot will determine whether Everton stay in the city or go.