The Yankees’ interest in free agent Matt Holliday is gaining legs, according to industry sources.

Holliday is a far cheaper alternative to Edwin Encarnacion, who could land a deal for $100 million and might be headed back to the Blue Jays. The Yankees also are interested in a reunion with switch-hitter Carlos Beltran and have contacted Mike Napoli’s representative.

The right-handed-hitting Holliday would fill the DH void created when Brian McCann was shipped to Houston and could give first baseman Greg Bird a break against lefties.

The Yankees’ interest likely doesn’t signify they are looking to deal left fielder Brett Gardner and use Holliday as Gardner’s replacement.

Holliday, who will be 37 in January, profiles for the Yankees as a DH/first baseman, though he has played 1,698 games in left.

Of course, this being the offseason, Gardner’s name surfaces in trade action. Yet the 33-year-old left fielder has two years and $25 million remaining on a very reasonable contract that includes a $12.5 million club option for 2019 (with a $2 million buyout and $1 million check if traded). And the Yankees’ only current replacement option to start the 2017 season in left is Aaron Hicks, who might be needed in right field if Aaron Judge struggles.

Gardner’s situation could change a year from now if outfield prospect Clint Frazier, received from the Indians in the Andrew Miller trade, is ready for the big leagues. Frazier likely will start the 2017 season at Triple-A.

“I have touched base with every bat,’’ general manager Brian Cashman said Wednesday afternoon, hours before a new five-year collective bargaining agreement was agreed upon.

With $136 million already on the books for next season, an estimated $40 million payout in arbitration, salaries for non-arbitration players and insurance premiums, the Yankees will likely exceed the new luxury tax with even one major free-agent signing or trade for a high-profile player. Reports had the threshold increasing from $189 million to around $195 million for the 2017 season.

Cashman is also focused on upgrading the Yankees’ rotation with veteran lefty Rich Hill (37 in March) on the radar. Hill, who appeared in 14 games as a reliever for the 2014 Yankees, is the best of a very shallow free-agent starter pool.

Hill, who had to work his way back to the big leagues via the independent league Long Island Ducks in 2014, went 12-5 with a 2.12 ERA in a combined 20 starts for the A’s and Dodgers this past season while battling a blister problem.

The Yankees also have expressed interest in lefty free-agent starter Derek Holland and are considered the favorites to land lefty closer Aroldis Chapman.

A strained right groin in 2015 and a fractured right thumb that required surgery in 2016 limited Holliday to 183 games the past two seasons.

However, he hit 20 homers and drove in 62 runs in 110 games last season, which ended seven-plus years with the Cardinals. He signed a seven-year, $120 million deal with the club before the 2010 season, and likely is looking at a one-year or one-year-plus-option deal this time.

Holliday, a seven-time All-Star (most recently voted in 2015) with a reputation as a positive influence in the clubhouse from his days in Colorado, Oakland and St. Louis, has played only 10 big league games at first base. He was the Cardinals’ Opening Day first baseman this past season, his first time in the big leagues at the position.

Yankee Stadium’s vast left field and the 6-foot-4, 240-pound Holliday aren’t a good marriage, but he might be able to navigate a much smaller right field in a pinch.

In 13 big league seasons (1,773 games), Holliday has 295 homers, 1,153 RBIs, a .303 average and .897 OPS.