The 2012 GOP nominee's advisers are examining what a fight at the convention might look like and what rules might need revising.
"It sounds like the plan is to lock the convention," said the source.
Romney is focused on suppressing Trump's delegate count to prevent him from accumulating the 1,237 delegates he needs to secure the nomination.
But implicit in Romney's request to his team to explore the possibility of a convention fight is his willingness to step in and carry the party's banner into the fall general election as the Republican nominee. Another name these sources mentioned was House Speaker Paul Ryan, Romney's running mate in 2012.
You don't have to read too far between the lines of the speech Romney gave Thursday at the University of Utah to see the imprint of this plan. He urged voters to support the candidate most likely to prevent Trump from racking up delegates in their states -- saying he'd back Florida Sen. Marco Rubio if he were voting in the Sunshine State, Gov. John Kasich if he were voting in Ohio, or Texas Sen. Ted Cruz in the states where he polls as Trump's strongest foe.
"If the other candidates can find common ground, I believe we can nominate a person who can win the general election and who will represent the values and policies of conservatism," Romney said.
According to the source, Romney does not expect Rubio, Cruz or Kasich to emerge as the single candidate that can accumulate 1,237 delegates and outright defeat Trump before the convention. So the only way to rob Trump of a victory would be to keep him from reaching that magic 1,237 number.
Most Republican states allocate their delegates proportionally, or in a hybrid format that gives delegates both to the statewide winner and at the congressional district level. This means rather than winnowing the competition down to a single Trump alternative, it could make more sense for all of the current candidates to stay in the race for a stop Trump movement, according to one source.
In addition, two senior Republican Party insiders told CNN that the convention scenario is now dominating a lot of conversation in GOP fundraising circles. To be sure, both of these sources are skeptical about Romney being able to execute this plan, but both believe that there is a real attempt underway to try to do this.
In the meantime, they said to look for Republicans like Romney to continue to cast doubt on Trump's business record and to keep pushing for him to release his tax returns.
"His bankruptcies have crushed small businesses and the men and women who worked for them," Romney said of Trump during his speech Thursday. "He inherited his business, he didn't create it. And whatever happened to Trump Airlines? How about Trump University? And then there's Trump Magazine and Trump Vodka and Trump Steaks, and Trump mortgage? A business genius he is not."
Asked by CNN's Wolf Blitzer about reports that Romney would try to block Trump at the convention, RNC Chairman Reince Priebus said he had not heard about that or had any conversations about that.
"Not really. This is the kind of conversation that's so far way from where this process is at. There are 1700+ more delegates to go," he said, adding later, "I just think it's a waste of time playing those matrix games right now."
If creating doubt about Trump's success starts to pay dividends and the convention plan were to come to fruition, these Republican Party insiders believe it will likely drive Trump into a third party candidacy in the fall.
Trump has repeatedly threatened an independent run if he isn't treated "fairly" by Republicans.
After Romney attacked Trump in a blistering speech Thursday morning, Trump hit back by mocking Romney's 2012 loss at a campaign rally in Portland, Maine -- pointing to Romney's efforts to secure Trump's endorsement.
"He was begging for my endorsement. I could have said, 'Mitt, drop to your knees' -- he would have dropped to his knees," he said.
He said of 2012: "That was a race, I have to say, folks, that should have been won. ... I don't know what happened to him. He disappeared. He disappeared. And I wasn't happy about it, I'll be honest, because I am not a fan of Barack Obama, because I backed Mitt Romney -- I backed Mitt Romney. You can see how loyal he is."
Trump said Romney thought about running again in 2016, but "chickened out."
CNN's Tom Lobianco contributed to this report.