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 ground's current Goodison Park site.
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 met with a good deal of opposition, in particular the newly formed Keep Everton In Our City group, which is actively campaigning against the move.
Bestway is now in talks with HOK Sport, which is currently working on the 2012 Olympic stadium in London, and engineers WSP Group, to draw up more detailed designs.