According to Jon Morosi and our own Chris Cotillo, the Diamondbacks have reached out and had discussions with Howie Kendrick, although a deal isn't close.
Source confirms: DBacks are in on Howie Kendrick but "no real progress" between sides yet. Other teams are involved. @jonmorosi mentioned.— Chris Cotillo (@ChrisCotillo) January 4, 2016
As of today, the Diamondbacks have Chris Owings, Aaron Hill, and Phil Gosselin splitting second base duties. Of that trio, only Gosselin posted an above average wRC+ in 2015, but he only has 261 career plate appearances, which makes it difficult to count on his performance last season. As for Owings and Hill, neither of them have provided any offensive value over the last two seasons, which is likely the reason for Arizona's interest in Kendrick.
Over the course of his ten seasons at the big league level, Kendrick has posted an above average wRC+ in seven of them, and twice finished with values of 98 (just two points below average).
Kendrick's market is unclear outside of the Diamondbacks, but as Cotillo reported, there are other teams interested in signing the free agent second baseman.
His former club, the Angels, seemingly have a need for a second baseman, as do the Padres. The Royals desperately need better production from their second basemen, but with $17.75 million committed to Omar Infante over the next two years, there isn't a lot of wiggle room for Dayton Moore to add someone like Kendrick.
There are still an abnormal amount of premier free agents on the market, but with spring training quickly approaching (44 days!), the dominoes should begin to fall rather quickly.