The Digital, Culture, Media and Sport (DCMS) Committee will hold a one-off evidence session on the future of Wembley on July 18.
Shahid Khan, the owner of Fulham and the Jacksonville Jaguars, has made the Football Association an £800 million offer to purchase the 80,000-seat stadium.
American billionaire Khan had been hopeful that he could complete a deal by August. However, the proposed sale, and how the FA would reinvest the windfall, have generated much debate.
The Daily Mail reported a potential stumbling block surrounding measures implemented to guarantee the FA's commitment to the stadium until 2057 following an injection of £161m from public bodies during its redevelopment, which was completed in 2007.
In a statement on Friday, the DCMS said the proposed sale of the "national asset" was a "move of considerable public importance."
Sports Minister Tracey Crouch has been invited to attend on July 18, along with representatives of both the FA and Sport England.
The chairman of the DCMS committee, Damian Collins, said: "Wembley is the home of English football, built in part using public money. There should be some public scrutiny of any decision to sell the stadium and how proceeds from this could be invested to benefit the long-term future of the game.
"The committee is interested in understanding the details of the FA's proposals and receiving evidence from people who may hold alternative views."