One week ago, an American League general manager was asked to predict which high-profile free agent would be the next to sign.

His answer: Yu Darvish .

The choice seemed especially logical after the Astros acquired Gerrit Cole , a move that should have propelled the Darvish sweepstakes toward a resolution. The Astros disappeared as a Darvish suitor, while clubs that had pursued Cole -- such as the Twins and Yankees -- were left with dwindling trade options, thus enhancing Darvish's appeal.

The atmosphere was ripe for a deal. Yet, Darvish remains unsigned.

The volume of interested teams is not the issue. The Yankees, Cubs, Twins, Rangers and Dodgers are involved in the Darvish pursuit, said sources, confirming a report by Jeff Wilson of the Fort Worth Star-Telegram.

The Twins -- with only three healthy, established starters on their Major League roster -- are almost certain to add an impact starter between now and the start of Spring Training. They have interest in Darvish, who would improve their chances of a repeat playoff berth in the final season before Joe Mauer and James Dozier become free agents. And with less than $50 million committed for 2019, the Twins can accommodate the addition of a high-priced ace over the long term.

The Brewers, who have been linked to the starting pitching market all offseason, are another team to watch. Milwaukee is expected to be without Jimmy Nelson for a portion of the 2018 season following shoulder surgery, although MLB.com's Adam McCalvy reported this week that Nelson is ahead of schedule in his recovery.

The Brewers have shown interest in right-hander Jacob Arrieta -- Darvish's foil in this offseason's free-agent market -- so it's not hard to envision Milwaukee pursuing Darvish, as well.

In a decision as consequential as signing Arrieta or Darvish, it's unclear how much general managers will consider the limited sample sizes of October baseball. Darvish is coming off a postseason in which he compiled a 6.14 ERA over four starts, including a loss in Game 7 of the World Series. Arrieta has a 3.08 ERA in nine career postseason starts.

Darvish confirmed via Twitter last week that the Yankees had made him an offer. The Yankees also are interested in adding a veteran third baseman, rather than start the season with young everyday players at both third and second base.

The Yankees may find it difficult to add Darvish and third baseman Todd Frazier through free agency, while remaining under the $197 million competitive balance tax threshold. The Yankees' current salary obligations for 2018 are roughly $163 million, according to the Cot's Baseball Contracts database.

Even after accounting for roughly $10 million in benefits and insurance -- as required in the CBT system -- the Yankees likely could add slightly more than $20 million to their current commitments and remain under the $197 million threshold. But the more they spend now, the less flexibility general manager Brian Cashman will have at the non-waiver Trade Deadline.

One possible explanation for the lack of a Darvish deal is the availability of right-handers Chris Archer (Rays) and Michael Fulmer (Tigers) on the trade market. Bill Brink of the Pittsburgh Post-Gazette reported last month that the Yankees had looked at both starting pitchers, and one source confirmed to MLB.com that the Tigers and Yankees have had trade discussions regarding Fulmer.

A separate source said the Rays have remained engaged in consistent trade talks regarding Archer in recent weeks. The Twins are viewed as a possible landing spot for Archer if they don't sign Darvish. The Cardinals also have spoken with the Rays about Archer, according to Derrick Goold of the St. Louis Post-Dispatch.

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