A Dallas Morning News report says the deal is believed to be worth more than $10 million.
Murphy, 32, hit .220 with 13 homers and 45 RBIs in 142 games for the Rangers in 2013. It was Murphy's sixth full season with the club. He joined them midway through the 2007 season as part of a trade deadline deal that sent reliever Eric Gagne to Boston.
Murphy's numbers in 2013 were the worst of his career and came one season after he batted .304 with 15 homers and 61 RBIs.
In 27 postseason games, Murphy hit .257, including a .412 average in the 2011 ALCS against the Detroit Tigers with a stout 1.147 OPS. He also recorded the final out of the 2011 World Series.
Murphy has a career .362 batting average (27-for-74) with three homers and 15 RBIs in 21 games at Progressive Field.