Everton's Goodison Park home and Liverpool's Anfield ground are separated by Stanley Park, but there has been talk for many years that the two Merseyside rivals should join forces to build a new venue.
The Toffees' own attempts to explore building a new stadium have failed to come to fruition and there have also been plans from Liverpool to expand Anfield.
However, while Moyes would be prepared to accept the two clubs playing in the same stadium, the Everton manager does not expect Liverpool to back such a project.
"We know we could do with some more cash and we would like a new stadium but we have an awful lot of things going for us," Moyes said on Talksport.
"I think Everton probably need a new stadium more than Liverpool but it is not something we have in our culture because we don't share grounds.
"It does make sense, we could really redevelop the whole area around Stanley Park. For us it is definitely worth doing.
"We'd take it but I don't think Liverpool would probably want us or need us and from that point of view I think that is where it will end up."
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