He has had three-days-a-week therapy since the end of the season and should be completely healthy long before the start of Spring Training.
Going into the offseason, he said he wanted to return to the Mariners and expected to be offered a contract for more than one year.
"I was informed by my agent [on Monday] that we were filing for free agency," Branyan said. "I was offered a one-year deal, but we felt it was pretty low and, quite honestly, we were looking for more than one year. He said [testing the market] was the only way we could get an idea of what my value is, so we rejected the offer."
The Mariners still have exclusive negotiating rights to Branyan until Nov. 20, leaving plenty of time to talk one-to-one.
"I would love to wake up tomorrow morning and hear that [Mariners general manager] Jack [Zduriencik] wants to go more than one year," Branyan said. "I'm tired of playing year-to-year. It's crazy. It's no secret that I would like to play the next two or three years in a Mariners uniform."
He remains hopeful that things will work out.
"My agent [Danny Lozano] said he's confident that we will get something done with Seattle," Branyan said. "He also told me not to take the [one-year offer] personally. It's just part of the negotiating process. He knows and the Mariners know I would take less to play there than somewhere else. All I want is to be treated fairly."
Meanwhile, it was reported by the News Tribune on Tuesday that the Mariners also had made a multiyear offer to shortstop Jack Wilson and it apparently was rejected, though club officials could not be reached to comment.
The Mariners have the choice of picking up the $8.4 million option for next season, buy out the final year of the deal for $600,000, or try to work out a new contract for the 31-year-old acquired from the Pirates on July 29 in a seven-player trade.
Injuries limited Wilson to 31 games with Seattle, and he batted .224 with one home run and eight RBIs after batting .267 with four home runs and 31 RBIs in 87 games with the Pirates.
There was no further news Tuesday on Ken Griffey Jr. His agent, Brian Goldberg, and the Mariners continue to discuss a one-year contract for the future Hall of Famer.