Cashman, though, is likely to continue shopping.
“The defending world champs happen to reside within our division as well as the previous year’s world champs within our league,” Cashman said on a conference call late Monday night. “So I think the American League is the elite league, so we have to find ways to close the gap.”
Cashman is seeking another starting pitcher, a middle infielder to cover for shortstop Didi Gregorius during his recovery from Tommy John surgery and replacements for the free-agent departures (at least for now) of relievers David Robertson and Zach Britton.
If the Yankees are intent on staying below the luxury-tax threshold again, Paxton’s contract will help. He is arbitration eligible and under contract for two more seasons, having earned $4.9 million last season.
The marquee free-agent starter on the market is the left-hander Patrick Corbin, who grew up in Clay, N.Y., outside Syracuse. Also available is J. A. Happ, who went 7-0 for the Yankees after arriving in a trade in late July but was rocked by the Red Sox in Game 1 of their A.L. division series.
The Mariners were willing to trade Paxton after once again failing to make the playoffs; Seattle has not reached the postseason since 2001. This month, General Manager Jerry Dipoto — who has acquired several Yankees prospects, including outfielder Ben Gamel and relievers James Pazos and Nick Rumbelow — said he was not rebuilding but retooling, trying to figure out how to compete in a competitive A.L. West.
“We don’t want to be trapped in perpetual mediocrity,” Dipoto said this month at the general managers’ meetings. “We’re trying to reimagine our roster. There has to be a different way.”
Along with Sheffield, the Mariners received a solid prospect in Swanson, 25, who was 8-2 with a 2.66 E.R.A. in Class AA and Class AAA this year, and a speedy outfielder in Thompson-Williams, 23, who hit 22 home runs in Class A.