Multiple media outlets reported the trade, but CBSSports.com first broke the story.
The deal cannot be finalized without Fielder's approval, as he has a limited no-trade clause in his contract that includes a provision barring a deal to Texas. He is expected to give his consent, according to multiple reports.
Fielder, 29, still has seven years and $168 million remaining on the nine-year, $214 million contract he signed with Detroit in January 2012.
Over his two years with the Tigers, Fielder hit .295 with a .387 on-base percentage, a .491 slugging percentage and averages of 27.5 homers and 107 RBIs. He played 162 games each year, was an All-Star both seasons and earned a Silver Slugger award in 2012.
Fielder began his career with the Milwaukee Brewers in 2005. From 2006-11 with the Brewers, he averaged 38 homers and 107.7 RBIs per year, earning three All-Star appearances.
The Rangers were looking for an offensive upgrade at first base after Mitch Moreland endured a disappointing season.
Kinsler, 31, has four years and $57 million remaining on his contract, plus a $10 million club option or a $5 million buyout for 2018. He signed a five-year, $75 million extension with Texas in April 2012.
A three-time All-Star, Kinsler hit .277 with a .344 on-base percentage, a .413 slugging percentage, 13 homers and 72 RBIs in 136 games this year. He would take over at second base for Detroit, replacing free agent Omar Infante.