The New York Yankees have been linked to just about every starting pitcher that’s been mentioned in trade rumors ahead of the July 31 deadline. The team is expected to improve its rotation within the next week, though acquiring one of their top choices could be difficult.

MLB Network’s Jon Heyman said on the latest edition of the “Big Time Baseball” podcast that the Yankees covet Noah Syndergaard more than any other pitcher. The right-hander has reportedly been pursued by both the Yankees and San Diego Padres, but he is considered much more likely to be dealt in the offseason than during the summer.

It also might be difficult for the Yankees to pry Syndergaard away from the New York Mets, who could inadvertently help their cross-town rivals win a World Series by agreeing to a trade. The Mets would probably require a massive asking price, one that the Yankees won’t meet.

The Yankees pursued Syndergaard last offseason and reportedly considered trading third baseman Miguel Andujar. 

Noah Syndergaard New York Mets Noah Syndergaard #34 of the New York Mets celebrates after defeating the Miami Marlins at Citi Field on September 30, 2018 in the Flushing neighborhood of the Queens borough of New York City. Photo: Adam Hunger/Getty Images

Of the pitchers that have a realistic chance of being sent to the Bronx before the 2019 MLB trade deadline, Trevor Bauer is atop the Yankees’ list, according to Heyman. He’s reportedly followed by Madison Bumgarner.

The odds of either pitcher being traded have seemingly plummeted within the last few weeks. 

The Cleveland Indians, once 10 games out of the AL Central, trail the Minnesota Twins by just three games in the division. The team has a two-game lead as the first AL Wild-Card team. Cleveland might need substantial major-league talent in order to trade Bauer since they are currently in the playoffs.

The San Francisco Giants don’t have nearly as good of a chance to make the postseason as Cleveland, but they find themselves in the thick off the race. After winning 16 of their last 19 games, San Francisco is two games back of the second NL Wild-Card spot. Don’t expect the Giants to give away one of the greatest pitchers in franchise history when he could potentially help them make noise in October.

According to multiple reports, the Yankees are hesitant to give up promising outfield prospect Clint Frazier in a deal for a pitcher who is not signed beyond the 2020 season. Bauer can become a free agent in a year and a half, while Bumgarner is set to become a free agent this winter.

Between the Yankees’ unwillingness to part with top prospects and what is happening in the playoff races, New York might ultimately have to settle for adding a pitcher that isn’t among their favorites.