The designs, drawn up by unnamed architects close to Bestway, have been put forward to try and show how a 50,000-seat stadium could be built on the site of Bestway's Scotland Road premises, known locally as 'The Loop'.
It is understood the club's chief executive Keith Wyness supports the 6km move northwards, not least because the scheme is being partly funded by supermarket giant, Tesco.
KSS' scheme would become incorporated into a larger Tesco development that would redevelop Kirkby town centre and create one of the country's largest Tesco Extra stores.
However, this decision has been met with a good deal of opposition, in particular from the newly formed Keep Everton In Our City group, which is actively campaigning against the move.
But one Everton shareholder and season ticket holder, John O'Donnell, believes that both schemes have to be weighed up equally.
'There is no use running headlong into the cheapest option, just because it's the cheapest option,' he said.
'We need to look at all options. The Bestway proposal is attractive as it is in Everton, but we have to wait for the costing.
'But these new schemes tell us nothing new. Bestway says they have drawn them up to show that a stadium will fit there, but we have known a stadium will fit on that site for weeks. The designs are just ugly,' he added.
Bestway is now in talks with HOK Sport, which is currently working on the Olympic Main Stadium, and engineers WSP Group to draw up more detailed designs.