– If a blockbuster trade involving Red Sox star Mookie Betts is to be made, the Twins might not be a part of it.

According to two sources with knowledge of the talks, the Twins were very pessimistic Saturday about their end of a proposed three-way deal with the Red Sox and Dodgers, a deal in which the Twins were to receive righthander Kenta Maeda from Los Angeles while sending righthander Brusdar Graterol to Boston.

Depsite losing faith that a deal could be struck, the Twins on Saturday made one last attempt to satisfy the Red Sox by offering a second minor leaguer — one outside their top 10 prospects — in addition to Graterol. With spring training set to begin this week, the Twins pushed Saturday for a resolution to the five-day saga.

The Twins hoped to resolve the situation by Saturday night, but did not set a hard deadline.

News about the deal broke Tuesday as the clubs exchanged medical records, a standard procedure before trades are finalized. Boston, after examining Graterol’s medical history, expressed concerns that his long-term role would be as a reliever and not a starter. The Red Sox asked the Twins to add an additional top-10 prospect to the deal.

While the Twins were excited about adding Maeda to their rotation, they were against sweetening the deal too much.

Meanwhile, Graterol, looking relaxed and smiling as he spoke with Twins coaches and teammates, threw in the bullpen for about 12 minutes on Saturday at the CenturyLink Sports Complex. He even flipped a baseball to an onlooker following his session. The Twins planned to use Graterol in the bullpen, where his 102-mile-per-hour fastball will be an asset.

Graterol was not made available to comment after his session. Twins pitchers and catchers officially report to camp Wednesday.

The Red Sox have received a lot of fan backlash about the possibility of trading Betts, their right fielder and the 2018 AL MVP, along with five-time All-Star pitcher David Price in a salary dump for what would amount to two prospects.

The Twins’ role would have enabled Boston to send Betts, Price and cash to Los Angeles in exchange for outfield prospect Alex Verdugo; Maeda would come to the Twins and Graterol would go to Boston. Betts is due $27 million in his final season before free agency, and Price has $96 million left on the three years of his contract. The Dodgers, in anticipation of that trade going through, lined up a deal with the Angels in which they send outfielder Joc Pederson and righthander Ross Stripling across town for infielder Luis Rengifo.

The Twins pulling out could topple all those plans in Jenga-like fashion, unless the Dodgers and Red Sox find a replacement for the Twins. Media reports during the past week indicated the entire deal was unlikely to fall through, but as time wore on it became apparent something was clearly wrong.

One report on Saturday indicated that the Twins and Dodgers could splinter off and work on a Maeda deal themselves.

Those close to the situation expressed their frustration as the drama surrounding one of the game’s elite players unfolded. Angels owner Arte Moreno, according to reports, expressed anger about his deal being delayed by the Betts saga.

Scott Boras, Graterol’s agent, took issue with Boston’s concerns about the health of his client, saying: “To suggest that this player is not healthy going forward, or has any form of substantive medical defect that would in any way damage his career, all of that is false. This is a scant supposition created by medical review, by someone who has never seen him physically.”

Tony Clark, head of the players’ association, even released a statement Friday. “The events of this last week have unfairly put several players’ lives in a state of limbo,” he said, demanding a quick resolution.

One person who was around Graterol the past week said the 21-year-old Venezuelan has been professional in getting his work done but that it was clear developments were on his mind.

The Twins were excited about added Maeda, who has an average fastball but a changeup that elicits swings and misses, and the Twins felt their speedy outfield was a good match for the flyball pitcher.

The Twins’ willingness to play a role in the megadeal shows they have not finished upgrading the rotation. They have Jose Berrios and Jake Odorizzi at the top of the rotation with free agent Homer Bailey currently set to be the No. 3 starter. Michael Pineda, after he completes his suspension for testing positive for a banned diuretic, and lefthander Rich Hill, once he is done with rehabilitation following elbow surgery, will fill out the rotation.

On paper, it’s a capable starting five topped by two righthanders who were All-Stars last July. Yet the Twins stepped forward as suitors for Maeda. That suggests they will have conversations about any quality starter who lands on the trade block between now and the July 31 trade deadline.