"We're not afraid to close with him, or with some other guys," A's manager Bob Melvin said. "Right now, there is no set closer, but he has put himself into position to be in there."
Johnson is one of three relievers who have saved games for the A's this season, joined by Luke Gregerson, who has three, and Sean Doolittle, who has one.
Johnson's recent streak dropped his ERA to 4.11, slightly better than Doolittle's 4.24.
The A's bullpen owns a 2.65 ERA, tops in the American League.
Doolittle's current streak of 29 innings without issuing a walk ranks fourth in Oakland history. He has also stranded his past 25 inherited runners, a streak that dates to June 22 of last year.
Rick Eymer is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.