The Chicago White Sox might have the American League's best record, but they still appear to be looking to add to their team.

Following the release of longtime left-hander John Danks on Tuesday, the White Sox could look outside the organization for a possible replacement, Bruce Levine of CBS Chicago reports. In addition, Levine hears from a source that Chicago is also "kicking the tires" on acquiring a quality left-handed bat.

"There is not a ton of activity in April and May," GM Rick Hahn said about the trade market. "You see the occasional player change hands. It's usually a depth move than a guy who will be there to go into a rotation. That stuff will heat up more in June and July."

In a separate tweet, Levine says that the team has been "very active" in its pursuit of additions.