The new structure is currently under consideration by the International Cricket Council (ICC).
The ICC is expected to make a decision soon on whether to implement the new format, which would involve promotion and relegation between two divisions of Test-playing nations.
While the idea has been floated as a way to improve competitiveness, Thompson argues it could severely hinder England's ability to play regular Test series against elite teams like India and Australia.
Thompson highlighted the significance of iconic rivalries, particularly the Ashes, as central to the global appeal of Test cricket.
Rather than introducing a potentially divisive tiered system, Thompson advocates for more strategic scheduling of bilateral Test series.
He believes this would create a fairer and more balanced WTC without jeopardising high-profile matchups that drive fan engagement and revenue.
"There's a lot of options that we've got to look at - tiers would be one of them," Richard Thompson told BBC Test Match Special.
"We wouldn't want, as England, if we go through a fallow period, to fall into Division Two and not play Australia or India. That simply couldn't happen. Common sense needs to prevail."