A source who has long been close to Romney believes the former Massachusetts governor and Republican presidential nominee will run for Senate later this year. Separately, NBC News reported that Romney wants to seek the Senate seat, citing a person familiar with his thinking.
Romney, 70, has been one of the harshest Republican critics of President Donald Trump. He is popular in Utah, the state where he now lives.
The former governor has slammed some of Trump's public comments and taken different stances from him on some foreign policy issues, particularly the U.S. relationship with Russia. However, he has long pushed for conservative economic principles.
Hatch, 83, announced his retirement Tuesday. It came just over a week after Trump signed the GOP tax plan that Hatch helped to craft into law.
In a statement Tuesday, Romney thanked Hatch for his service to Utah but did not address whether he would run for the Senate seat.
Trump had urged Hatch to remain in the Senate, and it is unclear if he would support Romney. On Tuesday, the White House would not commit to Trump backing the eventual Republican candidate for Hatch's seat.
Romney eviscerated Trump in a speech before last year's presidential election and also harshly criticized the president's response to violence at a white nationalist rally in Virginia earlier this year.
— CNBC's Larry Kudlow contributed reporting.