Labour MP for West Derby Ian Byrne has tabled an early day motion in the House of Commons regarding Everton's 10-point deduction imposed on them by the Premier League.
Mayor of Liverpool Steve Rotheram has also written to the Premier League to express his grievances with the decision to punish Everton in such a manner.
The Premier League announced on Friday that Everton were to be docked 10 points with immediate effect after an independent commission found them guilty of breaking the league's Profitability and Sustainability rules.
Such a sanction leaves the Toffees level on points with Burnley at the bottom of the table, plunging them back into the relegation dogfight.
Four wins in their last seven league games left Sean Dyche's side just one point off the top half, but attention will once again turn back to a scrap near the bottom.
In the motion table by MP Byrne, he requested the "suspension of all proceedings and sanctions made by the Commission until the regulator makes its own determination," adding: "This House condemns the grossly unjust points deduction imposed on Everton Football Club by a Premier League commission.
"(The motion) declares that sporting sanctions unfairly punish supporters and notices the improper dismissal of extraordinary mitigating circumstances outlined by Everton."
Mayor Rotheram was keen to point out in a letter to Richard Masters, the Premier League chief executive, that the punishment handed out to Everton did not fit the crime.
While acknowledging the need for strong regulation to uphold the league's sporting integrity, Rotheram made it clear that he sees the punishment as "wholly disproportionate".
Rotheram wrote: "While I understand, and indeed support, the importance of maintaining discipline and upholding the integrity of the sport, it is crucial to ensure that any punitive measures are proportionate and just. I do not believe that this punishment fits the crime.
"I completely support the club's appeal and would urge you to take a more lenient approach and consider alternative forms of punishment that do not unfairly penalise the club's players and supporters." Rotheram added.
Plans have been put in place by the UK Government to appoint an independent regulator to oversee the safeguarding of football clubs in the future.
Byrne believes that the events of the past few days means that this regulator must be established immediately.
Caroline Dinenage of the Department for Culture, Media and Sport said in the aftermath of the decision on Friday that it was "deeply disappointing for Everton fans, and for everyone who wants to see the English game thrive in a fair and sustainable way"
"It is clear the status quo cannot continue, and so I repeat my call for the Government to urgently introduce the Football Governance Bill, as announced in the King's Speech, to enable a statutory independent regulator to be in place as soon as possible." Dinenage added.
Everton return to action following the international break with a home clash with Manchester United on Sunday evening.