He will go before the Culture, Media and Sport committee after a series of claims by the Daily Telegraph.
The allegations have already led to Sam Allardyce losing his job as England manager.
The committee said recent events had shown "continuing major failings" in the system of football governance.
The FA's director of governance, Darren Bailey, will also give evidence at the hearing on 17 October.
Allardyce left his post last week after claims he told undercover reporters posing as businessmen how to "get around" player transfer rules.
Among other claims reported by the Telegraph, former Premier League manager Harry Redknapp is alleged to have said his players bet on the result of one of their matches.
The newspaper also claimed that eight current or ex-Premier League managers had taken bribes for player transfers.
The commons committee issued a strong statement saying it had "repeatedly urged the football authorities to improve self-governance".
"Although the committee's recommendations have been backed by successive sports ministers and progress has been promised by the FA, in practice very little has changed: the governance of football is cumbersome, and power lies with the clubs, especially in the Premier League," the statement said.
It added: "Real reform in relation to the ownership of clubs, transfers of players, the influence of fans, the role of agents and investment in the grassroots - amongst other issues - has stalled."
In the last Parliament, the committee recommended legislation to enforce good governance if no further progress had been made.
Following the revelations, ex-FA executive director David Davies said the FA was "screaming out to be reformed" while former FA chief executive David Bernstein, said the organisation produced "poor results" adding "it isn't a coincidence these things keep happening".
Chairman of the Football Association Greg Clarke has been called to face questions from MPs amid several cases of alleged corruption within the game.