The source said the deal won't become official until the completion of a physical.
A report in Miami's El Nuevo Herald, however, said the contract is for $32.5 million and includes an option for a fifth year.
In December, the White Sox exercised Ramirez's $2.75 million option for 2011.
Ramirez led American League shortstops this past season in batting average (.282), slugging percentage (.431), home runs (18) and total bases (252). He is the first shortstop in White Sox history to win a Silver Slugger Award.
Information from The Associated Press was used in this report.