Last year the Toffees revealed they were exploring locations for a new home in collaboration with Liverpool City Council.
And club chief executive Robert Elstone said at Everton's 2014 General Meeting on Tuesday that, while a series of sites were being examined, one - which he refused to name - was being focused on more than the others.
A team of external advisors, including planners, architects, designers and regeneration experts have been consulted on the proposed venture, with the viability of a new 50,000 capacity purpose-built ground inside the city boundaries of Liverpool under consideration.
Elstone said: "The stadium remains a big priority.
"We're not ruling out any of the sites that we've identified and that the council has presented to us, but there is one site which is getting more attention and has been getting more attention for a number of months.
"It has been worked on very carefully, diligently and in some detail by not only Everton, but by the council and by advisors, planners, architects, designers, cost consultants, regeneration experts and solicitors
So there's a lot of work going into something that we're very excited about.
"We need a council being supportive financially and supportive entrepreneurially as well
At the moment there are signs that they are being that, and that's to be welcomed and we're delighted with that.
"We hope it comes to fruition and, if it does, I think it's something that the city and our fans will be very proud of."
Elstone was keen to emphasise that the risks, and debt, associated with any move away from Goodison Park were being contemplated by the club.
He added: "The board is currently looking not only at this opportunity but also the associated risks and the debt that the club may well have to take on to deliver this, which may or may not be the right thing to do.
"That's exactly where we are in terms of the project at the moment - that consideration is ongoing by the board.
"But, in summary, there's a degree of optimism - perhaps some cautious optimism - but a degree of optimism.
"We wouldn't be investing what we're doing without thinking it had a chance of success, and there's a commitment as always to share information with our fans as soon as we can."
Source : PA
Source: PA