1) Jose Suarez
This should be an easy one. Teams are expressing interest in Jose Suarez and the Angels should have absolutely no issues giving him up. He showed this past season that he's not a pitcher the Angels can rely on in the future out of the rotation, and the bullpen isn't a much better spot either.
Suarez is receiving interest following a rough year for a variety of reasons. He's a left-handed pitcher who can start, has solid stuff, has had success in the past, and has three more years of club control. If there's anything teams value the most, it's team control.
The 26-year-old has been a decent back-end arm in the past and getting him in front of better pitching coaches could turn out to be a great thing for him. Even if he succeeds elsewhere it'd be the right move for the Angels to make to deal him.
Even if the Angels don't add another starting pitcher this offseason, Suarez still has no chance to crack the Opening Day rotation barring injury. A guy like Chase Silseth has certainly jumped him on the depth chart. Keeping him around as a long reliever wouldn't be the worst thing, but he'd have more value to the Angels with what he can bring back in a deal.
Suarez being out of options is what makes keeping him around so difficult. The only way the Angels could send him back down to the minors would be through waivers, and he'd certainly be claimed. Rather than lose him for nothing down the road, trade him for whatever you can get now. Of the five players on this list he's by far the most likely to actually go.