The Washington Nationals want to add an elite starting pitcher in a trade, according to major league sources. Rays left-hander David Price is an obvious possibility. But Tigers righty Max Scherzer would be an even better fit.

Think about it:

• Scherzer and Nationals general manager Mike Rizzo have a history — Scherzer was Rizzo’s last first-round pick as Diamondbacks scouting director, going No. 11 in 2006.

• The Nationals are deep in young power arms and veteran late-inning relievers, both of which surely are on Tigers GM David Dombrowski's wish list.

• The price in prospects for Scherzer, a free agent at the end of next season, would be lower than it is for Price, who is under club control for two more years.

• And, finally, the Nats maintain a strong relationship with Scherzer's agent, Scott Boras, and might stand a better chance of signing the pitcher long term than most clubs.

Does all this add up to a trade? At the moment, there is no way to know. For one thing, the Tigers' plans for Scherzer are not clear. At the very least, sources say, they are in the “listening, not shopping” mode. Translation: “Willing to move, for the right return.”

Trading Scherzer would give the Tigers payroll relief. Matt Swartz of MLBTradeRumors.com predicts that Scherzer will earn $13.6 million in his final year of arbitration.

Such a move also would open a spot in the rotation for left-hander Drew Smyly and enable the team to focus on an extension for third baseman Miguel Cabrera, whose current deal expires after the 2015 season.

Some rival executives, though, are baffled that the Tigers would even consider trading Scherzer, who is favored to win the American League Cy Young Award. A rotation of Scherzer and fellow right-handers Justin Verlander, Anibal Sanchez and Doug Fister could help the Tigers dominate the American League Central next season.

The Nationals’ rotation, meanwhile, is fronted by right-handers Stephen Strasburg and Jordan Zimmermann and left-hander Gio Gonzalez — and Strasburg is coming off surgery to remove bone chips from his surgically repaired right elbow.

Imagine what Scherzer would add that group.

Not bad.