"I spoke with Joe and his agent this morning, and expressed our interest in re-signing Joe," said Twins general manager Bill Smith. "We will remain in contact with them as we move forward into the free agent process."
Nathan, who turns 37 next month, returned this past season after Tommy John surgery wiped out his 2010 campaign. The right-hander made 48 appearances in 2011, going 2-1 with 14 saves and a 4.84 earned run average.
For his career, he has a 48-23 record with 261 saves and a 2.87 ERA in 581 games (29 starts) with San Francisco and Minnesota. Nathan has been with the Twins since 2004.