The person spoke on condition of anonymity because no announcement had been made.
Fielder signed a $214 million, nine-year contract with the Tigers before the 2012 season that includes a limited no-trade provision, and the big first baseman was set to approve the deal.
Kinsler just finished the first season of a $75 million, five-year contract.
The deal was first reported by CBSSports.com.
It's the first headline-grabbing move of baseball's offseason, and it involves two of the American League's top teams. Detroit has won three consecutive AL Central titles and reached the World Series in 2012, while Texas won the AL pennant in 2010 and 2011.
But neither team was about to stand pat. With stars like Fielder, Justin Verlander, Miguel Cabrera and Anibal Sanchez in the fold, Detroit's payroll had become one of the game's biggest, and although Fielder hit 55 home runs over the last two years for the Tigers, his numbers dipped this season and he struggled in the playoffs when Detroit lost to Boston in the AL championship series.
The trade could give Detroit more financial flexibility, with Cy Young Award winner Max Scherzer a year from free agency.
Fielder, however, is still only 29, and the Rangers would be adding a big bat to the middle of their lineup while also resolving a logjam in the middle of their infield. Jurickson Profar, a highly touted 20-year-old prospect, appeared to be blocked by Kinsler and shortstop Elvis Andrus. Now Profar should have a chance to play regularly.
The Tigers signed Fielder to a huge contract shortly before spring training in 2012 — after designated hitter Victor Martinez injured his knee. Martinez came back in 2013. With Fielder gone, Cabrera may move from third base back to first.
Kinsler fills a need at second base for Detroit after Omar Infante became a free agent.