Rivera, who turns 43 next month, suffered a season-ending injury May 3 in Kansas City, tearing his right anterior cruciate ligament. Rivera underwent surgery in June and is expected to be ready for Spring Training.
Baseball's all-time saves leader with 608, plus a record 42 more in the postseason, Rivera is currently a free agent after his two-year, $30 million contract expired.
It is likely that the Yankees will offer less than $15 million for the 2013 season, considering Rivera's age and the fact that he is coming off an injury.
But Cashman said that the Yankees trust Rivera can return to the closer's role, which he has filled in the Bronx since inheriting it from John Wetteland for the 1997 season.
"I believe in his ability to fill that job that he's always done," Cashman said. "He's never failed, and I know that knee is going to be good, so we look forward to returning him to the closer's role."
Rivera made just nine appearances this year, going 1-1 with a 2.16 ERA. In 2011, Rivera was 1-2 with a 1.91 ERA in 64 appearances, converting 44 saves, and he had saved at least 28 games in 15 consecutive seasons (1997-2011).
After Rivera's injury, the Yankees' closer job was held down by Rafael Soriano, who helped the club get to the postseason by converting 42 of 46 save opportunities. At the direction of agent Scott Boras, Soriano opted out of his contract last week, taking a $1.5 million buyout instead of a guaranteed $14 million salary for next season.
The Yankees issued Soriano a one-year, $13.3 million qualifying offer on Friday, along with identical offers for right-hander Hiroki Kuroda and right fielder Nick Swisher. Soriano and Swisher are expected to decline in favor of seeking multi-year deals on the open market; those three players have until Friday to accept or decline the offers.
"We have a qualifying offer on Soriano, so it's still possible we'll have him," Cashman said. "From our perspective, we're still in play."