"The first part of our offseason is going to be driven by retaining our own guys," Zaidi said.
The Dodgers made qualifying offers of $17.2 million for 2017 to Jansen and Turner, which requires signing teams to forfeit a Draft pick to the Dodgers and can put a damper on the players' attractiveness to other clubs.
• Hot Stove Tracker
That's particularly the case for Jansen, because the two other premier free-agent closers in this market -- Aroldis Chapman and Mark Melancon -- can be signed without clubs having to forfeit a Draft pick.
Zaidi stopped short of saying the Dodgers are determined to land one of the three top relievers, rather than trying to fill the position internally.
"Obviously, the way Kenley pitched in the postseason and the value of having that kind of guy in that setting, we and probably other teams out there are recognizing the value there," he said. "We have some guys that throw hard, have good stuff and are potentially closer candidates. But it's always best to have that guy that you can deploy early and often in the playoffs."
In contrast, there is not a comparable alternative to Turner on the market at third base.
"That's probably a spot where there aren't a ton of free-agent options," said Zaidi. "You either look internally or the trade route if it gets to that point."
After Hill's acquisition, the lefty pitched very well when he pitched, but finger blisters were an issue and made his availability unpredictable.
"With every potential free agent, you evaluate quality and durability," Zaidi said. "Those are the two key components. I don't think that's unique to him."
Blanton was the workhorse setup man, but finding him could embolden the front office to find the next one.
"The free-agent-reliever market is probably the segment of the market where there's the most volume and diversity," Zaidi said. "Guys coming off great seasons, guys coming off down seasons, hoping to find some value, a mechanical adjustment a guy might be able to make or a pitch-mix adjustment.
"That, as much as anywhere, is probably the place where a front office can spend the most time breaking down guys, just because there's such a diversity of arms. Depends on your need and internal options to a degree. If the need is more dire, you probably want more of a sure thing. If you feel like you're starting from a good starting point, you may be more willing to roll the dice on upside."
Zaidi said the club is "evaluating" whether to bring back Chase Utley, 37 and coming off a bounce-back year after an injury-riddled 2015. But Zaidi also said he's confident that Howie Kendrick, pushed to left field by Utley's play at second and injuries to outfielders, could return to second base in 2017. Kendrick has one year remaining on his contract, while Utley is a free agent.