Mike Napoli met with the Mariners this past week, and the free-agent catcher/first baseman is still talking to the club he may leave, the Rangers.
Rangers general manager Jon Daniels told The Dallas Morning News on Friday that "lines of communication remain open" between his club and Napoli.
Now, team No. 3 has a chance to make its pitch, according to CBS Sports.
Boston has a huge hole at first base after trading Adrian Gonzalez to Los Angeles in its house-cleaning blockbuster, and Napoli met with Red Sox brass this weekend, according to the Boston Globe.
Napoli, 31, has a combined 54 home runs the past two seasons, and he can play catcher, first base or serve as a designated hitter. Whichever team signs him will likely look at him as a hybrid rather than an anchor at one of those positions.
The sticking point in negotiations could be the difference between a three- and four-year deal, according to ESPN. Napoli's done great at Fenway Park in 24 career games, including the postseason. He has a .307/.404/.733 line with nine home runs and 20 RBIs in 75 at-bats.
The Mariners, meanwhile, want a middle-of-the-order bat in an otherwise young lineup.