Others such as Aston Villa, Tottenham and Everton, who may consider it unlikely they would ever drop out of a 20-team Premier League, may also have misgivings.
Mid-table clubs might also struggle to cope with a drop in television money as the cash is spread more widely.
In theory, any addition of the Old Firm to an English league could provide a stiffer test for Scotland's top two clubs and generate more enthusiasm from broadcasters and fans.
That would make up some of the money each club would lose if the Premier League is expanded from 20 to 36 clubs.
At the moment, teams relegated to the Championship are given £11.5m a year for two years because of the lost television income when they drop out of the top flight and are not promoted back into it.
Gartside's plan, which will need the approval of 14 out of 20 Premier League chairmen, would offer more financial stability to teams in the lower half of the Premier League, who would then be able to plan for the future with greater certainty.
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