Charles Dharapak/AP
Mitt Romney on the presidential campaign trail in 2012
Romney has been discussing the possible bid with top Republicans in Washington and Utah, according to a Thursday report in The Atlantic.
Hatch, who's 83 years old and the longest serving Republican in the Senate, is losing popularity among Utah voters, and the state's Republican leaders and donors are privately urging him to retire.
While Hatch says he hasn't made a final decision about whether he will run for another term - he called the speculation "premature" and "overhyped intrigue" - he told National Journal last week that Romney would be his ideal successor.
"If I could get a really outstanding person to run for my position, I might very well consider [retiring]," he said, adding, "Mitt Romney would be perfect."
Romney, who lost to President Barack Obama in the 2012 election, was an outspoken critic of President Donald Trump throughout the 2016 campaign, but he drew criticism when he courted the secretary of state position after the election.
Those who know Romney say he remains critical of the president and would "present a strong challenge" to the administration as a senator.
While Romney, now 70, called Belmont, Massachusetts home for many years, he has longstanding ties to Utah and has lived primarily in his house near Salt Lake City since 2015. As the first Mormon to win a major-party presidential nomination, he's widely popular in the state, which is home to the country's largest Mormon population.