Everton chairman Bill Kenwright has stated 'it is not an option' for the club to remain at Goodison Park.
Instead they are investigating the possibility of building a new stadium in Kirkby in partnership with Knowsley Council and supermarket giants Tesco.
Speaking at the annual meeting, Kenwright said: 'I do not want to be the guy who moves Everton away from Goodison Park. I did not want to be the guy that sold Wayne Rooney. I would love to say here forever.
'But it is not an financial option for Everton to remain at Goodison Park. I have also been told by the council it is absolutely impossible to extend the footprint of the club.
'As a board we have to make decisions and when we have made a decision we will go to the supporters.'
However, dozens of shareholders packed into the Brian Labone Suite rejected the idea in a hastily-conducted straw poll.
One said: 'Have the board thought about Everton leaving Liverpool and what that means to the supporters?
'It will be a long-term error to move out of the city limits. It will be a mistake to go to Kirkby.'
The theme continued with another stating: 'We will be putting up the white flag if we move to Kirkby. It will be a disaster and our fan base will be eroded.'
A third shareholder added: 'This is a bit radical. Why can't we move to south Liverpool? Surely that is an option.'
All three parties will look exclusively into the potential opportunities at Kirkby.
Everton say they will not explore any other possible sites at the moment but chief executive Keith Wyness stressed: 'No final decision has yet been taken.
'This option is just a possibility and one were are pursuing. We believe there is enough merit to examine the situation further and will continue to work hard with our partners.'
Everton also released an official statement which read: 'Everton Football Club have given their full commitment to investigating the feasibility of Kirkby becoming the home of their new stadium and will not explore any other possible sites at this time.
'The three parties will produce a joint business plan that considers all potential elements of the proposed development. This plan will then be reviewed to ensure that it represents the best way forward for all concerned including the local community.
'Everton, Tesco and Knowsley Council are fully committed to involving the community and local businesses in discussions over a potential development in the coming months.'
Everton's turnover for the 2005-2006 financial year was down from £60million to £58.1million but Kenwright, who was re-elected chairman, said 'it was a strong result'.
He added: 'Our drop down from a final placing of fourth to 11th last term cost us in terms of lost prize money and television money around £3.2million.
'So the fact that turnover has dropped by £1.9million, year on year, does represent a very strong result.'
The club showed a pre-tax loss of £10.8million compared to a profit of £23.5million the previous year when they sold Rooney to Manchester United for about £27million.
The wage bill increased by 20% from £30million to £37million while the net debt now stands at £21.8million
Meanwhile, the new £13million academy and first team base in Halewood is scheduled to open in the second half of next year.