Friday was the deadline for teams to make qualifying offers to players eligible for free agency and under terms of the collective bargaining agreement that offer must be the average of the top 125 salaries in baseball. For the 2013 season, that number turns out to be $13.3 million.
Players who do not receive a qualifying offer automatically become free agents, but can still sign with their current teams if a contract can be negotiated.
Hamilton has been a key factor in Texas reaching the playoffs the last three seasons with two of those years ending with World Series appearances.
He was named MVP in the American League in 2010 when he hit .359 and drove in 100 runs.
Hamilton got off to a tremendous start in 2012, but faded down the stretch -- a slump that coincided with the Rangers falling out of first place and losing the AL West title to Oakland on the final day of the season.
Hamilton finished with a .285 average, 43 home runs and 128 RBI. There had been speculation the Rangers were willing to part company with their star outfielder.
If any player turns down a qualifying offer, he becomes a free agent and his former team will receive a compensation draft pick at the end of the first round. Players have until Nov. 9 to accept or decline a qualifying offer.
Napoli fell from a .320 batting average in 2011 to .227 this year.
Kuroda is coming off his first year in the American League, during which he went 16-11 with a 3.32 earned run average in 33 regular-season starts.
Soriano and Swisher have reportedly decided to seek multiyear contracts with teams other than the Yankees.
Hunter, 37, hit a career-best .313 for the Angels this season.