Branyan is set to be the designated hitter in a minor league game on Tuesday. Depending on how he feels after that test, he could play first base on Wednesday.
"Russell hit in batting practice and took grounders," manager Manny Acta said Monday before the Indians played the Los Angeles Dodgers at night. "The plan is for him to play a few games on the minor league fields this week."
Signed to a one-year, $2 million contract on Feb. 23, the 34-year-old slugger has been sidelined with a herniated disc in his back and will open the season on the disabled list. Rookie Matt LaPorta will play first base when the Indians open against the White Sox in Chicago on April 5.
Branyan will accompany the Indians to Chicago, then join Triple-A Columbus on April 8.
"It's the smartest thing for both parties to continue to rehab and come back with a regimented schedule," Branyan said. "There's no sense in being selfish and rushing."
Branyan has battled back issues since signing with the Indians in 1994 and playing for nine major league teams. He said that no doctor has ever recommended surgery.
"This isn't going to take six weeks," Branyan said. "In the past, I've usually been ready after 35 at-bats. The thing we have to make sure of is withstanding the load of playing nine innings."
"I've been feeling good the last couple of weeks and thought I was going to be at this point earlier," he said.
Branyan was hitting .303 last July 1 for Seattle when his back flared up. He hit only .159 in July and .206 in August before being shut down, but still finished with career highs of 31 homers and 76 RBIs.
"I've had some of my best streaks with my back hurting," Branyan said. "We just have to see. The best-case scenario is that I go to Columbus and I feel I could be ready in seven to 10 days."