"There's no timetable," Melvin said about Johnson's possible return to the role. "Let's just get him straightened out. And we have plenty of options. That's the good thing about our team, our versatility. We'll play it by ear based on how the game's going, who's available on that particular day."
The A's traded for Johnson in December after they lost Grant Balfour to the Rays. Oakland is paying him $10 million this season and he'll be a free agent in the offseason.
The 30-year-old, who was an All-Star in 2012, allowed the Twins to tie Wednesday's game in the ninth inning after giving up two runs on two hits and two walks in only one-third of an inning. Oakland won the game in 11 innings.
Johnson has a 4.50 WHIP on the season.
"I'm trying to figure out what's going on," he said before Thursday's game in Minnesota. "The ball's not going where I want it to go consistently. Try to get it sorted out, try to get locked in. … I wish I had an answer."SI WIRE: Rays starter Matt Moore out at least a month with torn elbow ligament