The pending deal was for one year at $4.5 million-$5 million, the sources said.
The Web site MLBTradeRumors.com first reported the pact.
Kansas City acquired Crisp in a Nov. 2008 trade with Boston for right-hander Ramon Ramirez.
Crisp, a career .277 hitter, underwent season-ending rotator-cuff surgery to both shoulders in 2009 after appearing in only 49 games.
Kansas City declined an $8 million contract option with Crisp for 2010, making him a free agent.