The 33-year-old is hitting .299/.347/.443 with five home runs in 82 games this season, playing both corner outfield spots and DHing for Cleveland, all while hitting from the left side. Murphy is under contract for $6 million in 2015 and has a team option for 2016 that would pay him $7 million with a $500,000 buyout.
Cleveland is currently 45-52 and in last place in the AL Central and while they don't want to sell any of their long-term pieces like second baseman Jason Kipnis, it makes sense for them to move someone like Murphy, especially if they do not plan to pick up his option for next season.
The Angels, meanwhile, have a one-game lead in the AL West and a record of 55-43. However, they are severely lacking in production in left field, as offseason acquisition Matt Joyce is hitting .178/.275/.299 in 241 at bats this season. Los Angeles has also had a revolving door at DH this season, with Joyce and C.J. Cron, who is hitting .259/.285/.384 this season, taking the lion's share of the at bats there. In acquiring Murphy, the Angels would have what they thought they were getting when they signed Joyce.
Murphy would also provide balance to the Angels lineup, as four of the team's best five hitters, Mike Trout, Albert Pujols, David Freese and Johnny Giavotella, are right-handed. The only real left-handed threat in the Angels lineup currently is right fielder Kole Calhoun.
Adding Murphy would both balance and lengthen the Angels' lineup for what would likely be minimal cost in return and make them just that much more dangerous down the stretch and in October.