A trade of Noah Syndergaard this month is possible -- if a heavy price is paid.

While the Mets aren’t soliciting offers for Syndergaard, multiple teams have contacted them to express interest, sources say. The cost for the right-hander would have to be high for the Mets to consider trading him.

The Padres are among the teams that have inquired about Syndergaard’s availability recently, sources told MLB.com on Wednesday. San Diego’s farm system, rich with high-end pitching, will allow the club to seriously pursue virtually any available starter this month. The Padres have been looking for a veteran starter since last offseason, when they had interest in Syndergaard, Corey Kluber and Marcus Stroman, among others.

Another team monitoring Syndergaard and fellow starter Zack Wheeler are the Brewers, sources said.

The Mets, with the National League’s second-worst record, are viewed by the industry as a clear seller in advance of the July 31 Trade Deadline. That being the case, first-year general manager Brodie Van Wagenen is likely to move Wheeler this month, as Wheeler is on an expiring contract. Syndergaard, who won’t be eligible for free agency until after the 2021 season, is a less obvious trade candidate among Mets starters.

• Zack Wheeler trade rumors

Since the Mets have not committed to a full rebuild, they probably would need to acquire at least one Major League-ready starter for Syndergaard in order to justify moving him. A trade of Wheeler wouldn’t preclude the Mets from moving Syndergaard, too, since Wheeler isn’t being counted on as a long-term fixture in the rotation.

A trade match may prove difficult since the Mets are likely to base much of their valuation of Syndergaard on the 2.93 ERA he compiled over his first four Major League seasons. Interested GMs are more likely to reference his career-worst 4.68 ERA this season, although some clubs believe Syndergaard has great bounce-back potential.

Among the 45 pitchers who threw at least 100 innings in the first half, Syndergaard ranks ahead of only Wheeler and Ivan Nova in ERA+, according to Baseball-Reference.com. Controllable trade candidates Marcus Stroman, Matthew Boyd, Robbie Ray and Mike Leake all rank ahead of Syndergaard on that list.

In addition, there is pressure on the Mets to “win” any Syndergaard trade in light of the disappointing early returns from the Robinson Cano-Edwin Diaz trade.

Some within the Astros organization are intrigued by the possibility of acquiring Syndergaard, a hard-throwing Texan who could replace Gerrit Cole in future rotations if Cole leaves as a free agent this winter. Syndergaard is earning $6 million this season and is due to receive a raise in 2020, the first year he'll be eligible for arbitration.

Of the three Houston pitchers to have thrown more than 100 innings this season, only Justin Verlander is under contract to the club for 2020; Cole and left-hander Wade Miley are set to become free agents.

Syndergaard could potentially net a return similar to the packages that were dealt last year for Cole and Chris Archer, who, like Syndergaard, had two or more years of team control remaining.

In January 2018, the Pirates sent Cole to the Astros in exchange for right-hander Joe Musgrove, third baseman Colin Moran, reliever Michael Feliz and Minor League outfielder Jason Martin, who debuted this season and is rated as the organization’s No. 8 prospect, per MLB Pipeline. Cole has since emerged as one of the American League’s premier arms, making the All-Star team in each of the last two seasons.

The Pirates then acquired Archer from the Rays at last year’s Trade Deadline, sending outfielder Austin Meadows, right-hander Tyler Glasnow and a player to be named later (Minor league pitcher Shane Baz) to Tampa Bay. The trade seems lopsided in retrospect -- Archer has scuffled to a 5.49 ERA this season while Meadows is an All-Star and Glasnow was 6-1 with a 1.86 ERA before being sidelined in May with a right forearm strain -- but at the time, Pittsburgh hoped Archer could anchor the club’s rotation for years to come, like many of Sydnergaard’s suitors now envision.