Jose Pekerman's side are considered among the favourites for the South American showpiece, which begins in Chile in June, due to talents such as James Rodriguez, Radamel Falcao and Juan Cuadrado.
Colombia made the quarter-finals of the World Cup in Brazil last year, before exiting at the hands of the hosts, and will contest two friendlies this month as part of their build-up to the Copa.
Workouts against Bahrain and Kuwait are likely to represent the final opportunities for players to impress, with Adrian Ramos eager to nail down a starting place.
"Making the selection is motivating," explained the Borussia Dortmund striker.
"Being here motivates you and it makes you better prepared, with commitments such as the Copa America to come."
Ramos joined Andres Renteria, Jeison Murillo, Abel Aguilar, Carlos Sanchez, Juan Fernando Quintero and David Ospina in training on Monday, with the remainder of the squad due to arrive on Wednesday.
Rodriguez will not be joining them - having fractured a metatarsal in his right foot last month - although Falcao will likely get some much-needed playing time after struggling for minutes at Manchester United.
Pekerman defended the striker in a recent press conference and, while Falcao is all but guaranteed a Copa berth, Sanchez discussed the need to take these two friendlies seriously ahead of their competition opener against Venezuela.
"This call to the Colombia selection is very significant for all that will going to the Copa America," he added.
"The games here we will treat with respect and, like all the opponents we have faced, we will give them the same importance."
For Marjan Eid and Bahrain, Thursday's friendly will be their first outing since bowing out of the Asian Cup in January.
Defeats to Iran and United Arab Emirates saw them finish third in Pool C, with Eid's men also due to face the Philippines on Sunday.
Thursday's hosts face a difficult challenge in their first meeting with Colombia, with Pekerman's defence having been breached just twice in their last five matches.
One of those goals came in September's defeat to Brazil - Colombia's only loss since their World Cup adventure came to an end.
