NASHVILLE, Tenn. -- The Dodgers, reeling after losing superstar pitcher Zack Greinke to a division rival and to a lesser degree having a trade for top closer Aroldis Chapman derailed, have now joined the fray for star free-agent pitcher Johnny Cueto, sources say.

It didn't appear the Dodgers were targeting Cueto early in the free-agent game, but with Greinke gone to the rival Diamondbacks and David Price signed to the Red Sox, Cueto is the most obvious way to upgrade a rotation that has gone backward this winter, thanks to the disappointing departure of Greinke.

Cueto turned down a $120 million, six-year proposal from the Diamondbacks before they changed course and signed Greinke away from the Dodgers, and in a way that could benefit Cueto, as it opened up a spot in L.A. Cueto is said to have a couple other undisclosed teams in the mix. It isn't known who that is, but the Giants, Cardinals, Nationals, Orioles and his old Royals are among teams seeking a starting pitcher.

Johnny Cueto
The Dodgers are in on Johnny Cueto. (USATSI)

Cueto, 29, is in many ways a logical Greinke replacement since his lifetime ERA of 3.30 is actually slightly better than Greinke's 3.35, and his WHIP is an identical 1.18. The Dodgers are also believed to have some interest in Wei-Yin Chen but they are better set up to sign a right-hander since four of their starters are lefties.

The Dodgers have agreed to terms with fine veteran starter Hisashi Iwakuma in a deal that has yet to be announced, but the rotation is still where they've taken the biggest hit, thanks to the Greinke loss. They have the game's best pitcher Clayton Kershaw, plus Brett Anderson and Alex Wood, and they're hopeful for fairly timely returns out of pitchers Hyun-Jin Ryu and Brandon McCarthy -- both injured last season.

Cueto actually has posted the game's second best ERA to Kershaw since 2001 and was runner-up to him for Cy Young in 2014, but after a huge start with the Reds last year, he pitched unevenly with the Royals in the second half. He also has taken knocks for his postseason performance, but that is unfair: Cueto won the game Kansas City. had to win, Game 5 of the ALDS, and he pitched a complete-game victory in his World Series start, though he did have two other starts where he struggled.

The Dodgers do not appear to be in talks with the Yankees for Andrew Miller, as the New York's asking price is very high. Miller seemed like a logical target after the Chapman trade was derailed by news that he had an alleged domestic violence incident. While his lawyer Jay Resinger denied that the facts of the case are correct, the perception is such that Chapman is untouchable in trade now. That deal is considered on hold, but that's almost surely in an indefinite way.