Gwynn, who was injured during an offseason workout, is scheduled to throw for the first time on Thursday. He will undergo medical tests before a decision is made.
"We're like at a stalemate right now," said Gwynn, one of three candidates to be Milwaukee's fourth outfielder. "It's a touch-and-feel thing. We'll see how it feels when they bend my arm in different directions.
"It had progressed so well but now it seems to have plateaued. It could be a week. It could be a month," Gwynn added. "I guess if there is a good part, it's that if you are going to get injured, it's good to get it out of the way early."
The 26-year-old Gwynn made Milwaukee's opening day roster last year and had the game-winning sacrifice fly in a season-opening, 4-3 victory over the Chicago Cubs before sustaining a left hamstring injury that landed him on the disabled list April 9.
"It's going to be a while on his shoulder. The reports are that he is getting better. The definition of better is nebulous," Brewers manager Ken Macha said.
Gwynn, a Brewers draft pick in 2003, has played parts of three seasons in the majors. Last year, he hit .190 in 29 games with the Brewers and spent most of the season at Triple-A Nashville, where he batted .276 and had 20 stolen bases in 93 games.