The Premier League club are planning to leave Goodison Park and play their home games in a 50,000-seater stadium at a site that will also include new homes, education and health facilities.
Walton Hall Park is reportedly the preferred location, but the club have refused to confirm that is the case.
On Tuesday, Everton chief executive Robert Elstone said he has seen "signs" the council, who he described as a "key partner", are supporting the project.
And the body reacted on Wednesday by reiterating that they are behind the project, but are not in a position to pay for it.
A statement from Liverpool City Council read: "Following reports in the media today, we wish to reaffirm our commitment to working with Everton FC in relation to their new stadium proposals.
"As with all large-scale regeneration projects with the potential to create jobs and investment in Liverpool, the city council will look at ways it can support the wider regeneration scheme, but no firm options have been developed in terms of how or where this will take shape.
"This work is ongoing and we will announce the details of the location and support we will be offering once this has been further developed.
"However, we must stress that the city council is clearly not in a position to fund the costs of a new stadium.
"Any investment the council makes would be in a wider regeneration scheme, subject to a sound financial and economic rationale for doing so."
Elstone had spoken on Tuesday of the importance of the council's assistance in seeing the project through.
He said: "The key partner is Liverpool City Council. We're working very closely with them and they're being incredibly supportive.
"The public and private sector mix is important. Support from the public purse whether that's through grants or other forms of subsidy; and whether it's regional, national or European, we have to investigate all possibilities of securing public funding into the project.
"That’s one of the reasons why our scheme is so heavily focused on jobs and education and welfare; to essentially support and sustain those sorts of grants and subsidy moneys.
"We’ll need commercial partners alongside that to make the whole jigsaw fit together."
