If elected, the former Republican presidential nominee could clash with Trump on policies like relations with Russia and immigration.

Romney has been a prominent critic of President Donald Trump, but would likely find some areas of cooperation with him.

A Sen. Mitt Romney would bring the clout to rebuke President Donald Trump's most erratic behavior and some of his policies. Just don't expect him to disagree with the Republican Party too much if he wins Utah's Senate election in November. He didn't even mention Trump when he announced his plan Friday to run for the Senate seat vacated by Sen. Orrin Hatch. Romney, a Mormon who is popular in Utah, has a strong chance of becoming a senator, even if his previous experience in public office was in Massachusetts. The head of the Utah Republican Party and Democrat Jenny Wilson, who is running for Senate, have already criticized him as an outsider. Romney tweet The 2012 GOP presidential nominee would boast a national profile rarely seen from a first-term senator. The conservative Romney would likely agree with Trump on most issues, such as the GOP tax law passed late last year. Policies over which he could clash with Trump include national security, relations with Russia and immigration. "Utah welcomes legal immigrants from around the world. Washington sends immigrants a message of exclusion," Romney said in a video announcing his campaign Friday. The frequent Trump critic could also use his influence to criticize the president's divisive statements or work on bipartisan deals, according to two former Romney aides. But Romney would likely have to hold back some criticism of Trump, said Kevin Madden, who was a spokesman for Romney's 2008 and 2012 presidential campaigns. Trump remains highly popular among Republicans and Romney would be only one voice among 100 senators. "People are going to have to manage expectations about Romney serving as the premier or main counterbalance to Trump inside the party. A lot of people think that's going to happen automatically," said Madden, a partner at public affairs consulting firm Hamilton Place Strategies. Ryan Williams, another spokesman for Romney's 2012 campaign, added: "He's not going to be a daily critic of the president. But when there's something that rises to the level of where he feels the need to speak out, he'll do it." Romney would likely have a different relationship with the president than the outgoing Hatch, who has praised Trump in recent months. After the tax plan's passage in December, the senator called Trump "one heck of a leader." Trump reportedly begged the 83-year-old Hatch to run for re-election one more time. CNBC could not immediately reach Romney for comment.

Romney's policies

While Romney's positions could have shifted over the years, his 2012 campaign provides a guide to the stances he could take in Congress. Romney's policy positions could differ as he tries to appeal to a Utah electorate, rather than voters nationwide. He previewed some of his priorities in announcing his bid for Senate. Those include the national debt, trade, immigration and helping to restore civil discourse. "Utah has a lot to teach the politicians in Washington. Utah has balanced its budgets. Washington is buried in debt," Romney said. "Utah exports more abroad than it imports. Washington has that backwards. Utah welcomes legal immigrants from around the world. Washington sends immigrants a message of exclusion. And on Utah's Capitol Hill, people treat one another with respect." Madden notes that he would have to focus on some Utah-specific issues such as land use and the biotechnology sector, among others. In 2012, Romney adhered to fiscal conservatives' beliefs on the economy. He pledged to cut government spending and warned about the dangers of adding to the national debt. The Trump administration and current GOP-controlled Congress appear to have abandoned those tenets. They are expected to contribute to the growing debt with their recently passed tax plan, which they followed up with a deal on massive spending increases this month. Romney pledged to repeal the Affordable Care Act and push back against its provisions that critics say infringe on religious freedom. While some consider the health-care plan Romney implemented in Massachusetts as a precursor to Obamacare, Romney called for states to craft their own health-care plans. Some current GOP lawmakers have pushed for similar health policy. The former governor could break with Trump in two notable areas. In 2012, Romney famously called Russia the biggest geopolitical foe the United States faces. Since Trump became president, lawmakers on both sides of the aisle have argued he has not responded forcefully enough to Russia's efforts to interfere in the 2016 election. Romney could become another one of those members of Congress. He did not mention national security policy in his campaign announcement. And though the 2012 GOP presidential nominee pushed for increased border security and a fence on the southern border — an area where he agrees with Trump and many other Republicans — he also championed lower barriers to legal entry for highly skilled immigrants and stressed the importance of keeping families together. Trump is currently pushing for major restrictions on legal immigration and limits on extended family reunification. It is unclear where Romney would stand now on the Obama-era Deferred Action for Childhood Arrivals, a program that protects nearly 800,000 young undocumented immigrants from deportation. Trump ended the program in September with a six-month delay, and Congress is struggling to find a solution to shield the immigrants brought to the U.S. illegally as children.

Romney's influence and relationship with Trump