In a quiet holiday week, the Mets are getting a better idea about the free-agent bullpen landscape.

One proven reliever is imperative to augment Jeurys Familia, AJ Ramos and Jerry Blevins in the late innings next season. Ideally, general manager Sandy Alderson — who has spoken about his desire to limit many of his starting pitchers’ exposure to two times through the batting order — would add two bullpen arms.

The Mets, according to industry sources, are very interested in Bryan Shaw, who spent the last five seasons under new manager Mickey Callaway’s guidance with the Indians. But team officials are also keeping tabs on Joe Smith, Mike Minor and Addison Reed, among others.

Shaw, 30, is a workhorse — he led the AL in appearances three of the last four seasons — and would give the Mets flexibility in the seventh and eighth innings. The right-hander went 4-6 with a 3.52 ERA and 1.213 WHIP in 79 appearances last season for the Indians, where Callaway was the pitching coach.

Smith, who previously pitched for the Mets, is highly regarded by team brass and would probably require a lesser commitment in terms of dollars and contract length. But there is some belief the veteran righty, an Ohio native, might prefer to remain with the Indians, even for less than market value, to stay anchored to his roots.

In 59 appearances last season, split between the Blue Jays and Indians, the 33-year-old Smith went 3-0 with a 3.33 ERA and 1.037 WHIP. The Mets previously had interest in Smith at the trade deadline in 2016.

Minor is a top lefty option, whose ties to new pitching coach Dave Eiland add to his luster. Minor went 6-6 with a 2.55 ERA and 1.017 WHIP last season for the Royals, with Eiland as the pitching coach.

And Reed is familiar to the Mets from his parts of three seasons with the club, during which he was the team’s most consistent reliever. His tenure ended on July 31, when he was dealt to the Red Sox for minor-league relievers Gerson Bautista, Jamie Callahan and Stephen Nogosek.

Familia’s absence last season — he missed three months recovering from surgery to remove a blood clot from his right shoulder — only underscored to team officials the importance of bullpen depth. Paul Sewald provided help in small doses, but the Mets were largely disappointed by a cast that included free-agent bust Fernando Salas, Hansel Robles, Josh Smoker and Erik Goeddel.

The Mets signed outfielder Zach Borenstein to a minor league contract and invited him to spring training. Borenstein, 27, spent last season at Triple-A for the Diamondbacks.