Jansen, 29, recovered 47 saves and posted a 1.83 ERA and a sparkling 0.670 WHIP for the Dodgers in 2016. He struck out 104 and walked only 11 hitters in 68.2 innings.
Sources also indicate the Dodgers are close to a deal to retain free agent third baseman Justin Turner. Joel Sherman of the New York Post reports the sides are discussing a four-year deal in the $64 million range.
Turner, 32, had his best year in 2016, hitting .275/.339/.493 with 27 home runs, 34 doubles and 90 RBIs in a career-best 151 games.
How do these moves affect the White Sox? Well, it means the Dodgers are no longer a likely trading partner for the South Siders, because the Dodgers have no need for two of the players the Sox are trying to trade -- closer David Robertson and third baseman Todd Frazier.
With Jansen's signing, all the major free agent closers are off the board. The New York Yankees signed Aroldis Chapman (5 years, 86.5 million), and the San Francisco Giants picked up Mark Melancon (4 years, $62 million) during the winter meetings last week.
The losers in the Jansen sweepstakes -- notably the Washington Nationals and Miami Marlins -- could be potential landing spots for Robertson, who is owed $25 million over the remaining two years of his contract.
Other free agent possibilities for teams shopping for closers include Greg Holland -- who recorded 125 saves from 2013-15 in Kansas City, but did not pitch in 2016 after arm surgery -- and Brad Ziegler, an eight-year veteran with 85 career saves who finished last year in a set-up role with the Boston Red Sox.
If Holland is healthy -- a big if -- his upside is better than Robertson's at this stage, but Robertson's durability makes him less of a risk for teams. Robertson has appeared in at least 60 games for seven consecutive seasons. The same is true for Ziegler -- his stuff isn't as dynamic as a healthy Holland, but he's appeared in 64 games or more for eight consecutive seasons.
If the Dodgers settle up with Turner, we know Frazier won't be traded to Los Angeles, but where might he go?
How about San Francisco? At the end of last season, the Giants were counting on Eduardo Nunez and Conor Gillaspie at third base. It turns out Gillaspie had some big hits for the Giants during the postseason, but as all Sox fans know, Gillaspie is best utilized as a left-handed bench bat, not as an everyday third baseman. Frazier is an upgrade over Nunez or Gillaspie.
Boston also would be a possibility. The Red Sox traded third baseman Travis Shaw to the Milwaukee Brewers to acquire the eighth-inning reliever they needed in Tyler Thornburg. People have been saying that opens the door for Pablo Sandoval to be the Boston third baseman in 2017. OK, I suppose, but do the Red Sox really want to count on 140 to 150 games from Sandoval in a season where they are trying to win a championship? I'm skeptical.
Lastly, don't count out St. Louis. The Cardinals showed they are serious about making a push in 2017 with their five-year, $82 million commitment to center fielder Dexter Fowler. But they still appear to be a bat short. Some of the big free agent hitters out there -- notably Edwin Encarnacion and Mark Trumbo -- are DH types who are more suitable to the American League. Frazier, in contrast, can actually play his position well, and he represents a potential upgrade both offensive and defensively over Jhonny Peralta. Frazier has only one year left on his contract, so the risk would be minimal for St. Louis.
The best available free agent third baseman right now? It's Luis Valbuena. Teams would rather have Frazier, I'm sure.