Could signing Clayton Kershaw be a no-win situation for Dodgers?

“Pitchers break.”

That was the rational side of Mark Walter’s brain speaking. You know, before the Dodgers’ chairman agreed to sign right-hander Zack Greinke to a guaranteed $147-million, six-year contract.

Which worked out well in the first year of his deal, and leaves you wondering exactly where they are headed with left-handed ace Clayton Kershaw.

Kershaw, 25, is going to become stupidly rich, the only question being exactly how stupidly rich. He is arbitration-eligible for 2014, and then if the Dodgers don’t sign him to a long-term deal, he can become a free agent after next season.

Kershaw has been tight-lipped about contract talks with the team, so it’s difficult to get a definitive feel for where he’s at. It would be easy to pick up mixed signals from his comments to The Times’ Dylan Hernandez on Saturday, when he said both that he was “curious” about looming free agency and yet “open-minded” about contract talks with the Dodgers.

At first you just assume the Dodgers will ultimately work this out because, you know, they sort of have to. Walter and his Guggenheim group have already pushed the Dodgers to a record payroll and it’s hard to fathom that they would let a rare prize like Kershaw get away.

Yet it’s not hard to make the argument that the attempted signing of Kershaw looms as a no-win situation for the Dodgers.

ESPN’s Buster Olney reported two weeks ago that the Dodgers offered Kershaw a lifetime contract in the range of $300 million last season. Kershaw would not comment on the report to Hernandez.

Let’s take a breath here. For $300 million you could almost buy the Tampa Bay Rays. Even in these bizarrely fluid economic times in baseball, that’s a difficult number to fathom.

The record contract for a pitcher is the $180-million extension the Tigers gave Justin Verlander. Earlier this year, the Mariners signed Felix Hernandez to a seven-year, $175-million deal. The all-time record contract is the 10-year, $275-million contract Alex Rodriguez signed with the Yankees, now considered by many as the single worst contract in sports history.

Kershaw brings something of a dilemma to the Dodgers. While it’s pretty much understood he’s going to surpass the contracts of Verlander (who’s five years older) and Hernandez (two years older), at what point do the numbers become ludicrous?

Remember, “pitchers break.” Kershaw threw almost 275 innings last season. And in 2012 he had to overcome foot and hip issues.

Still, Kershaw offers a unique package for the Dodgers. He is on the verge of winning a second Cy Young, has a great work ethic, came up through the Dodgers system, is great in the clubhouse and community, is intelligent and mature beyond his years, is still approaching his prime and just generally seems to offer a link to the old-school O’Malley past that — let’s face it — appeals to a large portion of the team demographic.

How could the Dodgers possibly let him go?

“We already know we have to give him a lot of money,” co-owner Magic Johnson said last month. “What’s a few more zeros?”

Are clubs really signing elite pitchers to seven-year deals and expecting them to be healthy and effective the length of their contracts, or just feeling that’s the going rate?

If the Dodgers sign Kershaw for seven or 10 years, or whatever constitutes a lifetime contract, what are the odds he avoids serious injury the length of the deal? And if they don’t sign him, what are the chances the fan base forgives them?