The person spoke on condition of anonymity to The Associated Press because the agreement has not been announced.
The 35-year-old Martinez had perhaps his best season career in 2014, hitting .335 with 32 home runs and 103 RBIs and helping Detroit to its fourth straight AL Central title.
The switch-hitter has hit over .300 in eight of his last nine seasons, not counting 2012, which he missed because of a knee injury. His bat carried the Tigers at times in 2014, when Miguel Cabrera slipped slightly from his MVP form.
AP Sports Writer Ronald Blum contributed to this report.