"I think any player, that's the reward of baseball, to make it to that point," Kershaw said. "I think any player gets curious when you get close, for sure."
That doesn't mean Kershaw will ever test the open market. Co-owner Magic Johnson said last month that he was confident the Dodgers and Kershaw would come to an agreement on a multiyear deal this winter.
Asked if he was hopeful the situation could be resolved soon, Kershaw replied, "I really don't know what to expect. I'm just kind of open-minded going into the off-season. Whatever happens, I'll be coming back next year anyway. I'm just trying to prepare for that."
Kershaw, 25, will be eligible for salary arbitration for the last time next season. He is expected to win his second Cy Young Award this month.
Kershaw and his wife, Ellen, were in Torrance on Saturday night to be honored by Sharefest, which runs after-school programs supported by his foundation. Kershaw will be recognized Sunday by Westcoast Sports Associates, which offers athletic opportunities to at-risk children in Southern California.
Considering his ties to the community, could he see himself playing his entire career in L.A.? "I don't really think about that," he said. " But I love it here. Ellen and I, we feel comfortable here."
ESPN reported that during the season, the Dodgers offered Kershaw "essentially a lifetime contract in the range of $300 million." Because Kershaw was uncertain about making such a commitment and reluctant to engage in serious negotiations during the season, the talks were never completed, according to the report.
Kershaw declined to comment.
"I think I'm going to hold up my end of the bargain and not talk about it," Kershaw said. "I don't know where all that stuff's coming from, but I don't necessarily appreciate that it's out there."
As for his spectacular 2013 season, Kershaw said the way it ended tainted the experience. Kershaw was the losing pitcher in the 9-0 defeat to the St. Louis Cardinals that eliminated the Dodgers from the National League Championship Series.
"It's always tough when you end the season on a loss like that," he said. "It just ends so suddenly. Obviously, I didn't pitch as well as I would have wanted to. It's not always easy to look back. You try and think of all the positives, but you do have a bitter taste in your mouth."
Kershaw said he watched the World Series.
"I didn't think I would, but, yeah," he said. "I think it was because my buddies wanted to watch it more than anything. I didn't have too much sentiment either way. But when you see anyone celebrate, you want to do that."
Kershaw said the key for the Dodgers next season will be to remain healthy.
"When we have all our guys on the field at the same time, we're one of the best teams," he said. "We proved that. I think, for us, that has to be our main concern."
Kershaw and his wife will return later this month to Africa, where they have built an orphanage. They intend to build classrooms this year.