Per MLB Network's Jon Heyman, there's a sense that the Red Sox are "more serious than ever" about a trade, and rival teams "are starting to think" the 2018 American League MVP will be dealt.
Heyman noted there's no indication which team is the most likely destination.
Kevin Acee of the San Diego Union-Tribune reported Monday that the San Diego Padres would part with Wil Myers, two young major leaguers and one prospect.
The two big leaguers would include a combination of one outfielder between Manuel Margot and Josh Naylor and one starting pitcher between Cal Quantrill and Joey Lucchesi.
Acee noted the Padres feel the chances that the deal will happen are "marginally possible." The Red Sox also want San Diego to pick up half of the $67.5 million still owed to Myers, but the Padres are only willing to chip in 25 percent of that contract.
Per Alex Speier of the Boston Globe, the Red Sox remain in discussions with the Los Angeles Dodgers about a potential deal involving Betts.
Betts, who is in his final season of team control, agreed to a one-year deal worth $27 million on Jan. 10. The 27-year-old is a four-time All-Star and hit .295/.391/.524 with 29 homers last season.