Robertson, the most talked about of Nats trade options, actually likely could've been traded to the Nationals last winter around the time the Nats acquired Adam Eaton if not for Mike Rizzo's unwillingness to deal Victor Robles. Robertson is posting a 3.38ERA with a 3-2 record and 9 Saves in 21.1 Innings of work so far this year. Robertson is set to make $12 Million this year and $13 million next year before hitting free agency after 2018.
Colome is my personal favorite. The 28 Year Old Dominican set the world on fire last year collecting 37 saves with a 1.91ERA in 56.2 Innings in his first year of closing. Colome is a bit of a gamble admittedly, only having 53 career saves, but is looking good if not better than last year posting a 1.96ERA and 16 Saves through 26 appearances this year. Colome has the extreme upside of not being a FA until 2021, but will not be cheap.
Likelihood: Mid-High if Rays sell, Low if they don't.
The Royals are selling this year and expect it soon. Herrera(27) Has been closing for the Royals ever since Wade Davis was dealt to the Cubs, and is one of the few players left from the 2015 World Champion Royals. Though he didn't close Herrera threw 5 innings with 1 unearned run in the 2015 World Series. Herrera hasn't been great this year however currently posting a 4.13ERA in 24 innings but won't be a FA until after 2018. Mike Rizzo might be able to steal one here with the Royals mid collapse.
Likelihood: Very High
Osuna has recently been getting things on track after being temporarily being removed from the Blue Jays closing role. The 22 year old was a stud last year posting a 2.68ERA and 36 Saves over 74 Innings. The Blue Jays have been teetering with rebuilding with key players leaving and getting older, don't expect them to sell the mexican star if they can keep it together. Osuna won't be a free agent until 2021.
In closing, any of these high end closers will do fine on the 37-21 Nationals, adding any of these revilers will just send them higher up into the stratosphere.