He wrote: "With the nation so divided, resentful and angry, presidential leadership in qualities of character is indispensable".
In a Washington Post essay published on Tuesday evening, Romney said Trump's presidency "made a deep descent" in December and blamed him for the departures of defence secretary Jim Mattis and White House chief of staff John Kelly. "But I pointed out, there are places where we agree on a whole series of policy fronts, but there are places that I think the president can - if you will, elevate his game".
Arizona senator Mr Flake tweeted with a link to the article: "A thoughtful piece by incoming Senator Romney".
"The world needs American leadership, and it is in America's interest to provide it", he wrote.
Romney will be sworn in Thursday along with the rest of the incoming Senate by Vice President Mike Pence.
Romney changed his mind about Trump later on, calling the then-president elect a "man who can lead the United States to a better future", back in November 2016.
During an appearance on Fox News early Wednesday, David Bossie, a senior Trump campaign aide in 2016, said he feared that Romney was positioning himself to be a potent Trump critic in the Senate.
Democratic Sen. Dick Durbin, D-Ill., said he suspects the 2020 elections will prompt more Republican senators to confront Trump when they disagree with him, and that may already be happening, citing recent actions on Saudi Arabia. His op-ed was a shallow political miscalculation and a pathetic attempt to be the center of attention. Trump wrote on Twitter, appearing to reference outgoing U.S. senator Jeff Flake, one of the few Republican lawmakers who publicly spoke out against Trump, at the cost of drawing the president's wrath. He won. And I recognize that and appreciate that. He said later: "I would vote for the border wall. He should be happy for all Republicans", the president wrote. "Best wishes for our duly elected president: May his victory speech be his guide and preserving the Republic his aim", he wrote on Twitter.
McDaniel, a MI political operative and daughter of Romney's older brother Scott, used to go by her full name - Ronna Romney McDaniel - professionally, but stopped using her maiden name upon becoming the RNC chair following the 2016 election.
But this is where Trump is at his worst, Romney says.