Shapiro only said that they would "get" a reliever, so the next move could be a trade or a free agent signing. If the Indians decide to go the trade route, the only team actively shopping a closer is the Phillies with Jonathan Papelbon. A number of other teams could have other relievers available with experience closing games, but it would be difficult to pinpoint specific names.
On the free agent market, there are a few notable relievers who have saved games in the past, including John Axford, Andrew Bailey, Joaquin Benoit and Grant Balfour. Other former closers who are current free agents include David Aardsma, Alfredo Aceves, Octavio Dotel, Kyle Farnsworth, Frank Francisco, Mike Gonzalez, Kevin Gregg, Joel Hanrahan, Ryan Madson, Carlos Marmol, Fernando Rodney, and more.
Former Indians closer Chris Perez is also a free agent after being released by the team earlier in the offseason. His departure likely stands as one reason the team feels the need for someone with experience finishing out games. The team is heading into 2014 without an established closer and doesn't have a clear internal candidate to fill the position. By signing an arm, they can at the very least have someone who has saved a number of games come in to compete for the job in spring training.