Dodgers proceed slowly on Zack Greinke

NASHVILLE — The Dodgers are taking a measured approach in their pursuit of pitcher Zack Greinke.

The Dodgers haven’t made an offer to Greinke or any other free agent, and their top targets appear to be taking their time deciding where they will play next season.

“I think everybody is in diligence mode right now,” Dodgers General Manager Ned Colletti said.

Meanwhile, the Dodgers are becoming increasingly uncertain about whether their efforts to re-establish a presence in Asia will result in the signings of two pitchers, South Korean All-Star Ryu Hyun-jin and Japanese teenager Shohei Otani.

Colletti sounded pessimistic Monday about the Dodgers signing Ryu, though his negative tone could be a negotiating ploy. The Dodgers bid $25.7 million to win a league-wide auction for the rights to negotiate with Ryu, a left-hander they project as a No. 3 or No. 4 starter. They have until Sunday to strike a deal. If they don’t, they will be refunded their posting fee and Ryu will return to his team in South Korea.

In the case of Otani, 18, the Dodgers’ skepticism doesn’t sound like a negotiating ploy. The right-hander has a fastball that has been clocked in the 99-100-mph range and the Dodgers have scouted him since his first year of high school.

One club official said he would be “shocked” if Otani came to the United States and signed with a team other than the Dodgers, but it is not clear that Otani will leave his homeland.

Otani held a news conference in October, where he announced his intention to go directly from high school to the United States rather than play in the Japanese league. Nonetheless, Otani was selected by the Nippon-Ham Fighters in the first round of the Japanese draft.

The Fighters have spent the last month trying to convince Otani to sign with them, and their efforts might be working. After meeting with the club Monday, Otani told reporters in Japan, “I appreciate how the team erased my concerns. I want to be able to give them an answer in the next week.”

If Otani remains in Japan, he would probably start next season in the country’s top league. If he comes to the United States, he would probably be sent to rookie ball.

The Fighters have offered Otani a $1.2-million signing bonus, plus $600,000 in incentives, the maximum contract a Japanese team can offer an amateur player. They have also offered Otani the No. 11 jersey that was worn by Yu Darvish, who now pitches for the Texas Rangers.

Because of Major League Baseball’s collective bargaining agreement, the Dodgers are allowed to spend $2.9 million on international amateur players. If their total spending is 15% over that limit — which it would likely be if they sign Otani — they would be prohibited from spending more than $250,000 on any international amateur player next year.

dylan.hernandez@latimes.com