Sports Illustrated reported the deal will likely include a full no-trade clause for the 27-year-old slugger, who hit .324 and led the National League with 39 home runs and 126 RBI last season.
Fox Sports said the deal was all but wrapped up, pending a physical for Kemp.
The six-year veteran, who has one year left on his current contract, also stole 40 bases and set a career high with a .586 slugging percentage in 2011.
Since his rookie year in 2006, he has averaged 26 home runs and 30 stolen bases with a career .294 batting average.
Celebrity Families of 2014 [PHOTOS]