All 72 clubs in the National League have signed a letter to EFL chiefs asking them to back a vote of member clubs over changing to a three-up, three-down system between League Two and the fifth tier.
National League clubs argue that the current system, where only one club gets automatic promotion to the EFL with a second place available through the play-offs, is inconsistent with the rest of the pyramid.
The Red Dragons are on course for an astonishing third successive promotion after clambering out of the National League, through League Two and towards the Championship.
Wrexham are fighting for promotion alongside League One's biggest spenders Birmingham City, who count NFL legend Tom Brady as a minority investor.
Shrewsbury sit second bottom of League One but one of their six wins of the season came against Phil Parkinson's side 2-1 in January.
