Dodgers are said to be close to deal with Zack Greinke

The Dodgers are close to making free agent Zack Greinke the highest-paid right-handed pitcher in baseball history.

While a contract wasn’t finalized on Saturday night, the two sides were nearing a deal that would pay Greinke $147 million over six years, according to people familiar with the situation who weren’t authorized to discuss it publicly.

The record contract for a right-handed pitcher is a five-year, $112.5-million extension Matt Cain signed with the San Francisco Giants in April. The most lucrative deal for any pitcher was the seven-year, $161-million contract left-hander CC Sabathia signed with the New York Yankees four winters ago.

If the deal with Greinke is completed, the newly rich Dodgers’ salary commitments for 2013 would already be close to $220 million, the most in baseball. That figure doesn’t include the salaries of arbitration-eligible players or deferred payments owed to players no longer on the team.

The Dodgers opened the 2012 season with a payroll of less than $100 million.

The franchise has taken on close to $600 million in salary commitments since it was purchased by Guggenheim Baseball Management last spring.

From a baseball standpoint, the addition of Greinke would give the Dodgers a front-line starter to complement ace Clayton Kershaw at the top of the rotation.

“Best 1-2 combo in baseball!” first baseman Adrian Gonzalez posted on his Twitter account.

Greinke, 29, is the clear-cut No. 1 pitcher on the free-agent market.

He had his best season in 2009 with the Kansas City Royals, when he won the American League Cy Young Award and was 16-8 with a 2.16 earned-run average.

He pitched for the Milwaukee Brewers and Angels in 2012, and was a combined 15-5 with a 3.48 ERA in 34 starts. Over nine major league seasons, Greinke is 91-78 with a 3.77 ERA.

But Greinke’s past also includes battles with social anxiety disorder and depression.

Drafted with the sixth overall pick of the 2002 draft, Greinke considered leaving baseball when he was in the minor leagues. He considered it again in the spring of 2006, when he broke down after a wild throwing session and left the team. The incident led Greinke to seek medical help. He started to take antidepressants and his condition improved.

People who know Greinke describe him as sometimes aloof but highly intelligent.

“Zack was one of the most interesting players that I’ve had and one of the most enjoyable players that I’ve had,” Brewers Manager Ron Roenicke said. “He’s brutally honest and he’s going to make some comments at times that you’re not going to be happy about. Then he turns around a couple days later and you talk and all of a sudden you’re laughing and really enjoying the guy.

“He doesn’t care for a lot of fluff talk. He doesn’t care how the weather is outside. He wants to know how his slider can get nastier. That’s what he wants to know. When you talk to him about those things that interest him, you’re in for a great conversation.”

Even without Greinke, the Dodgers have six veteran starting pitchers under contract for next year: Kershaw, Chad Billingsley, Josh Beckett, Ted Lilly, Chris Capuano and Aaron Harang.

Capuano and Harang figure to be the most likely candidates to be traded.

The Dodgers could add yet another starting pitcher before the end of the weekend, as they continue to negotiate with South Korean left-hander Ryu Hyun-jin.

The Dodgers’ exclusive negotiating window with Ryu closes at 2 p.m. Sunday. If Ryu doesn’t sign, he will return to his Korean league team, the Hanwha Eagles.

dylan.hernandez@latimes.com