Sosa hit 21 home runs with 92 RBIs this season with Texas. He sat out in 2006, and the Rangers gave him a $500,000 minor league contract.
"I feel victorious, and I think I proved that I have what it takes to stay in the major leagues," he said at a news conference.
The 38-year-old outfielder said he expects several offers next week when teams begin negotiations with free agents. Sosa had recently said he wanted to be back with Texas next year.
Sosa finished the year with 609 home runs. He was the fifth player to reach 600, joining Barry Bonds, Hank Aaron, Babe Ruth and Willie Mays.
"If they let me, I will reach 700," he said.
Sosa did not see a lot of action after the All-Star Game.
"It was devastating when manager Ron Washington called me into his office and told me they were going to cut back my playing time," he said. "My reaction was to go home and quit."
Sosa finished with a .252 average in 114 games, including 87 starts as a designated hitter.