A parliamentary inquiry into Bury’s financial crisis and expulsion from the Football League is set to take place this autumn.
The Shakers were expelled from the Football League, losing their place in League One, after C&N Sporting Risk pulled out of a proposed takeover of the club last month.
Damian Collins MP, who is the chair of the Department for Digital, Culture, Media and Sport committee, says hearings will be held which will also examine "the role of the EFL and the FA in safeguarding the long-term interests of clubs".
In a statement, Collins called for fit and proper person's tests to be strengthened, for football's governing bodies to have the power to get involved earlier when member clubs encounter financial difficulties and for the EFL to find a way to reinstate Bury to the Football League for next season.
"The decision by the English Football League (EFL) to expel Bury football club is a tragedy for all who follow the team as well as the wider community that it serves. It also marks a failure of football governance," Collins said in a statement.
"The current owners and directors test is clearly not sufficient to protect the long-term interests of clubs and keep bad owners and directors out of the game.
"The football authorities need greater powers to intervene earlier when clubs get into financial difficulties, and certainly long before they get to the edge of the abyss."
He added: "I would ask that even at this late stage that the EFL considers any realistic proposal that could support Bury's status as a Football League club, including whether they could play next season in League Two, under new ownership.
"The select committee believes that the issues that have affected Bury reflect a wider and growing problem within the Football League. We have seen similar crises at Bolton and other clubs in recent years.
"The committee has therefore agreed that we will hold hearings in the autumn to take evidence relating to the crisis at Bury, and the role of the EFL and the FA in safeguarding the long-term interests of clubs. The committee will also inquire into what needs to be done to strengthen football governance rules in this regard."