New York announced its decision Friday, five days after it lost the World Series to the Kansas City Royals.
The 30-year-old homered in a record six straight postseason games but then slumped in the Series, hitting .150 (3 for 20) and making key errors in Games 4 and 5. He batted .281 during the regular season with 73 RBIs and a career-best 14 homers.
Murphy, who became a free agent after the Series, has until Nov. 13 to accept.
If a team made a qualifying offer to a player who signs a major league contract with another club before the June amateur draft, his former club would receive a draft pick as compensation at the end of the first round.
The team signing that player loses its first-round pick in the amateur draft, unless that pick is among the top 10, in which case the club loses its next-highest pick.
New York also said outfielder Michael Cuddyer underwent surgery Thursday at the Vincera Institute in Philadelphia to repair a core muscle injury.