Amy Coney Barrett emerges as Trump's favorite for Supreme Court

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2:33

(CNN) ––

Justice Amy Coney Barrett has emerged as President Donald Trump's big favorite to replace the late Supreme Court Justice Ruth Bader Ginsburg, according to several people familiar with the deliberations.

These sources even added that the president's opinion was solidified during a long meeting at the White House on Monday.

Trump has yet to make a final decision.

And, with the days until he announces his election this Saturday, his consideration could change.

At the moment, the White House is working on scheduling a meeting between Trump and Judge Barbara Lagoa, two sources told CNN.

Just as long as the president is in the Miami area on Friday.

• LEE: Barbara Lagoa, one of Trump's main candidates for the Supreme Court of Justice

Lagoa is one of five female candidates the president has considered as Ginsburg's replacement on the Supreme Court.

However, two sources said that Lagoa's chances have dropped significantly since the weekend.

For now, Barrett, who sits on the United States Court of Appeals for the Seventh Circuit in Chicago, is Trump's clear favorite.

She is also considered within the White House as the likely candidate.

The president announced this Tuesday morning that he will announce his election to the Supreme Court this Saturday at the White House.

Amy Coney Barrett vs.

Barbara lagoa

Officials said Trump seemed very enthusiastic about Amy Coney Barrett after they met for several hours.

Then the president told several people that she believes Barrett will be very well received by "her people," according to an official.

Now, no one close to the process dares to say that Barrett is the chosen one.

But, Trump gives the impression of being completely convinced of her.

A source familiar with Trump's private conversations told CNN that one of his confidants on the matter mentioned to him that this decision is very important: not only for his legacy but also for his bid for re-election.

He even pointed out to the president that she effectively "will be his new running mate," according to the source.

The judge of Cuban origin who could arrive at Court 3:40

Lagoa remains on the list.

Still, several people familiar with the matter told CNN that the idea of ​​electing her fades with Trump.

While the president was enthusiastic about the prospect of electing a Cuban-American from Florida - a state in contention for the White House race - Lagoa has not previously been examined for the Supreme Court.

Also, some advisers suggested that it would be a great effort to clear a new name quickly.

The White House can still schedule a meeting with Lagoa.

However, two sources said her chances have dimmed significantly since the weekend.

The other candidates

On Monday, Trump initially said he was considering five names for the Supreme Court vacancy, before adding that he was really focusing on just "one or two" names.

Others on the list are federal appeals court judges Joan Larsen and Allison Jones Rushing, as well as Deputy White House attorney Kate Todd.

But they are not considered serious contenders.

Especially after it became known in the White House that Larsen volunteered for Joe Biden's presidential campaign in 1987.

• LOOK: The Republican Party begins to line up for a quick confirmation vote of Trump's candidate for the Supreme Court

Trump maintained that the date to announce his candidate this weekend was intended to show respect for Ginsburg.

The judge will remain on the Supreme Court this Wednesday and Thursday, before a private burial at Arlington National Cemetery next week.

However, the president is also interested in extending the drama of his selection.

He even described this decision as his version of choosing a running mate in an election year, according to an adviser.

The suspense of the announcement for the Supreme Court

Trump plans to make his announcement during a primetime speech, according to the adviser.

Just as he did with Neil Gorsuch and Brett Kavanaugh early in his tenure.

Previously, the president has reveled in the drama of the moment.

In fact, there was an attempt to convince the media that he had selected Thomas Hardiman over Gorsuch in 2018, by having Hardiman leave his home and drive to Washington.

This time, Trump has been clearer about who is on his list and how many names he seriously considers.

He praised Lagoa during an interview on Fox News.

Yet even some of those in favor - of whom there are many in Florida Republican circles and among Trump's political advisers - acknowledge that Barrett is leading the charge.

The impact of Ruth Bader Ginsburg's death on Court 4:17

Decision factors

Cuban Americans are an important part of Trump's reelection coalition.

However, Lagoa poses a problem for some court-focused conservatives: his ties to the Bush family, which according to one source is viewed with skepticism by some Republicans.

This is because President George HW Bush appointed Supreme Court Justice David Souter, who was expected to be a Conservative but voted with the liberal wing.

Another factor weighing on Trump's decision, at least in part, is Republican Senator Josh Hawley.

The legislator has said that his support for a Supreme Court justice depends on whether the candidate believes that Roe vs.

Wade (the case that allowed the possibility of abortion) is "badly decided."

Hawley said Monday that Amy Coney Barrett "meets that standard."

But she added that she is less certain with the views on abortion that Lagoa defends and is something that she is still reviewing.

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  The fight for a new judge on the Supreme Court adds a surprising twist to a presidential election in crisis

"I don't know the answer to that," Hawley argued.

Hawley said he spoke to the White House about his views over the weekend.

Now that Republican Senator Mitt Romney of Utah has shown signs of agreeing to a vote before the election, everything seems to indicate that any candidate will be confirmed, except for possible stumbling blocks of the chosen one during the confirmation process.

Dana Bash and Kristen Holmes, both from CNN, contributed to this report.

Candidates United States Supreme Court Donald Trump Ruth Bader Ginsburg