Members are to vote on the nomination at CME's annual meeting May 7, the company said in a release on its Web site.
Hastert served in the U.S. House of Representatives from 1987 to 2007, representing Illinois's 14th Congressional District and was Speaker of the House from 1999 to 2007.
Former Assistant Secretary of the Treasury for Financial Markets Timothy Bitsberger was also nominated for a position on the board. Bitsberger is treasurer and senior vice president of the Federal Home Loan Mortgage Corp. -- Freddie Mac.
CME Chief Executive Officer Craig Donohue and five other current directors were also nominated.