PHILADELPHIA -- The Phillies said they took their best shot at signing a Japanese superstar.

News broke late Thursday night that right-hander Yoshinobu Yamamoto reportedly agreed to a record-setting 12-year, $325 million contract with the Dodgers. Phillies president of baseball operations Dave Dombrowski, as well as other sources, said the Phils made a strong enough offer to believe they were legitimate contenders, along with the Dodgers, Yankees and Mets.

“I think we were extremely competitive,” Dombrowski said. “We were very, very competitive. We were aggressive. When we made our presentation [last week in Los Angeles], I think our guys did a tremendous job. I think they presented the organization well.”

Sources declined to reveal the Phillies’ final offer, but the deeper they got into negotiations, the more they realized Yamamoto simply preferred Los Angeles and New York over Philadelphia.

Perhaps no amount of money could have changed that.

“I don’t think it had anything to do with anything else, he just preferred to be a Dodger,” Dombrowski said. “Ultimately he was just not a person attuned to coming to Philly.”

But the Phillies tried anyway because they considered Yamamoto a unique opportunity. He is an elite-level starting pitcher who is just 25 years old.

“That’s why we jumped in,” Dombrowski said.

The Phillies were involved from the very beginning of the offseason. When they signed Aaron Nola to a seven-year, $172 million contract in November, they said publicly that any future roster improvements would be mostly complementary (i.e. rotation, bullpen and possibly outfield depth). But sources said they would make an exception for Yamamoto, even if they considered themselves longshots.

The Phillies always fought long odds to sign Yamamoto. Not only because of his affinity for L.A. and New York, but because they didn’t expect to compete with the Dodgers, Yankees, Mets and other teams, who seemed to have more money and more motivation to sign him. The Mets reportedly offered $325 million. The Yankees reportedly offered $300 million.

But the Phils became more comfortable with the money required after last week’s meeting with Yamamoto went well.

“We were optimistic,” Dombrowski said. “We thought we had potential for it to happen, yes. We had ownership support. John Middleton and our ownership group were very supportive of it.”

So now what?

“It’s more around the edges, trying to get our club better,” Dombrowski said.

It means rotation and bullpen depth. (Free agents like Blake Snell, Josh Hader, etc., remain highly unlikely.) There had been some thought the Phillies would try to sign an outfielder to provide insurance in case center fielder Johan Rojas struggled. But the Phils do not want to block an opportunity for Rojas by signing someone who expects regular playing time.

Any outfielder the Phillies might add, Dombrowski said, “Might be going around the edges.”

Besides relatively modest upgrades, sources said the No. 1 priority is signing ace Zack Wheeler to a contract extension. It is something they always planned to pursue, even if they got lucky enough to sign Yamamoto.

Wheeler is eligible to become a free agent following next season.