If you've ever listened to sports radio in New York, you've undoubtedly heard somebody call the station and propose a trade between the Yankees and Mets.

The host will listen, make his or her comment about why it makes sense and would help both teams, thank the listener for their call and move on, knowing full well that any such trade is never going to happen.

The Yankees and Mets just don't do business with each other. But they should. And they should start right now.

Whether it's the fear of a prospect thriving on the other side of town or executives worried about the optics of helping their crosstown rival get to the postseason -- or even worse, win a championship -- there has been major hesitation between the two teams to make trades during their 55 years of cohabitation in New York.

There have been only 16 trades between the two teams, the most recent coming in December 2014 when the Mets sent right-hander Gonzalez Germen to the Yankees in exchange for cash considerations. Prior to that, the two teams hadn't completed a deal since 2004, when Mike Stanton was traded to the Mets for Felix Heredia in a swap of lefty relievers.

The most significant deal between the two teams came after the 2001 season, when the Mets sent third baseman Robin Ventura to the Yankees in exchange for outfielder David Justice. Ventura was an All-Star in '02 before being traded the following summer, while Justice never played for the Mets, who flipped him to Oakland a week after acquiring him.

With the two teams headed in different directions this season, a look at their rosters suggests they could help each other. Would general managers Brian Cashman and Sandy Alderson take that chance? Could they convince their respective owners that dealing with the other team in town is the best approach to getting their own clubs where they want to go?

Forgetting all of the inner-city politics that would come along with such trades, here are some suggestions for deals that would be beneficial for both the Yankees and Mets. We'll leave the politics to somebody else.

1. Lucas Duda for Austin Romine

First base has been a black hole for the Yankees this season, and although they finally cut the cord on Chris Carter by designating him for assignment last week, the position remains in limbo thanks to Greg Bird's uncertain health.

Christopher Austin is a temporary fix, but doesn't feel like the long-term answer for 2017. Duda, who is headed for free agency next season, would provide stability at the position, not to mention the power lefty bat the Yankees were expecting Bird to be this season. Duda has nine home runs and a strong .961 OPS since May 25, which is more than 300 points higher than the collective OPS of Yankees first basemen this season. He wouldn't be asked to carry the lineup, but rather take aim at the short right-field porch in the lower third of the batting order, alleviating the pressure of trading in his blue and orange for pinstripes.

Romine would be a loss for the Yankees, but you've got to give to get. The 28-year-old has excelled behind the plate this season as Gary Sanchez 's backup (and as the starter during Sanchez's month-long stay on the DL), but he'll be due another raise in arbitration this offseason and is destined to play second fiddle behind Sanchez as long as he's here. Kyle Higashioka showed in April he can adequately handle backup duties.

Travis d'Arnaud has two years of team control remaining, but his constant injury issues and underperformance has to be wearing on the Mets' front office. Romine would provide better defense behind the plate when he plays and possibly light a fire under d'Arnaud, who may be running out of time in Queens.

2) Jerry Blevins and/or Addison Reed for Dustin Fowler

Fowler, ranked as the Yankees' No. 8 prospect by MLB Pipeline, is having a terrific season at Triple-A Scranton/Wilkes-Barre; the 22-year-old ranks in the top 10 in the International League in home runs, stolen bases, OPS and runs scored.

With a glut of outfielders ahead of him in the Yankees' system -- Clint Frazier and Blake Rutherford are the club's Nos. 2 and 3 prospects, respectively, while Aaron Judge , Aaron Hicks , Brett Gardner and Jacoby Ellsbury are locked in for at least another year at the big league level -- Fowler doesn't appear to have a place with the Yankees.

The Mets, on the other hand, have only Yoenis Cespedes and Michael Conforto signed in the outfield beyond this season -- unless you count Juan Lagares , who can't seem to stay healthy and on the field. Fowler, a solid center fielder who continues to grow at the position, would allow the Mets to move Conforto to right field on a full-time basis.

Tyler Clippard allowed four earned runs over his first 25 appearances this season, posting a minuscule 1.57 ERA through June 3. His season turned nightmarish over the past three weeks, however, as he's given up runs in six of his past nine outings, blowing two leads while posting a 16.20 ERA during that stretch. He's given up nine runs in just 1 1/3 innings over three appearances in the past week. Yikes.

With Clippard struggling and Adam Warren dealing with shoulder inflammation, the Yankees' bullpen could use some help. Reed will be a free agent this offseason, while Blevins has a $7 million club option for 2018 with a $1 million buyout, making both attractive trade candidates for the two sides.

3. Curtis Granderson for Austin

Granderson's days as a productive player appeared to be over a month ago, but he's rebounded with a stellar four-week stretch, posting a .351/.463/.675 slash line with six home runs over his past 26 games.

Hicks' oblique injury will keep him on the DL for about a month, and even though Ellsbury is back from his concussion, he's shown an inability to stay on the field every day. In addition to rotating with Ellsbury, Granderson could also serve as a part-time DH when Matthew Holliday plays first base.

Granderson performed well at Yankee Stadium during his first stint in pinstripes and would be welcomed back by the fans, which is something to consider when bringing a member of the crosstown rivals to the Bronx.

As for Austin, he would give the Mets a young, versatile player who could play either corner-outfield spot or first base. The Yankees would have to find a new first baseman, but since they've already traded for Duda in this world, that's already been addressed. Isn't it nice when things work out?