It appears to be a two-team race for Kris Bryant between the Philadelphia Phillies and the Colorado Rockies.

Bryce Harper is continuing to push management to sign his good friend in Bryant, someone he grew up with in Las Vegas.
"Harper is really pushing Dave Dombrowski, the president of baseball operations, to sign him," says MLB analyst Jim Bowden. "It appears right now—after Seattle made that trade with Cincinnati yesterday—it appear it is down to Colorado or Philadelphia for Kris Bryant."
Bowden also reports that the Rockies are in "intense" negotiations with Bryant, and ownership is now involved.
"Kris Bryant and the Colorado Rockies are intense negotiations right now. Bryant could take a shorter deal there and regain his value by playing half of his game in Coors Field."