Crain's Chicago Business reports the 31-year-old Republican lawmaker is interested in the job.
The election isn't until 2014, but Crain's reports the political maneuvering has already started.
Illinois Treasurer Dan Rutherford of Pontiac and State Senator Bill Brady are also said to be interested in running in 2014. They're also Republicans.
A spokesman for Schock tells WMBD 31 news the congressman has no plans to run for governor, but hasn't taken anything off the table.
The spokesman says right now Schock is focused on rising in the U.S. House of Representatives.