Liverpool City Council is being urged to do all it can to keep Everton based within the city perimeter.
Remaining at Goodison is not a financial option, the club says
The Premiership club is considering moving to a new purpose-built stadium in neighbouring Knowsley.
Former Labour Minister Peter Kilfoyle said the city council had failed to offer the club any "realistic sites" for its proposed stadium in Liverpool.
But the authority said it had discussed two possible sites with the club and was keen for it to stay in the city.
In a Commons motion on Wednesday, the MP praised Knowsley Council for its "positive" backing.
An Everton fan, whose Walton constituency covers Goodison Park, Mr Kilfoyle is now urging the city to provide "meaningful support" for what he says is a "local, national and international club."
Knowsley Council is carrying out a public consultation on its regeneration plans, which include Everton's move to Kirkby.
The club could build a 55,000-seater ground in a town centre development that will also include shops, a hotel and a supermarket.
Everton FC said an alternative to Goodison Park would increase capacity and improve corporate facilities.
A Liverpool City Council spokesman said: "We are keen to see Everton stay in the city and we have discussed two potential sites with the club that we believe could meet their needs.
"Everton have an exclusivity agreement with Knowsley which means that they are concentrating on exploring that option at the moment, but we are in regular contact with the club."