Melvin will still continue to rely on matchups for the ninth inning, meaning Johnson will be considered with fellow righties Luke Gregerson and Dan Otero and southpaw Sean Doolittle.
Johnson has not allowed a run over his last five outings, and opponents are hitting just .200 against him during that stretch. He allowed at least two runs in three of his first five appearances for a 18.90 ERA.
"Nothing's for sure and we're still operating under what we feel are the best matchups, but we've seen him later in games, and there's still potential for that," Melvin said. "He's throwing a lot better than he did earlier in the season, there's no doubt about that. The sinker's down in the zone, he's throwing more strikes, his mechanics look a lot cleaner."
Ryan Cook's outings have also been encouraging, since the right-hander was lifted off the disabled list April 7. But he's still slowly being worked back into high-leverage situations, after missing most of Spring Training with shoulder issues, so he's not considered a current option to close games, Melvin said.
Cook has allowed just two hits in 6 2/3 innings, but he's also walked six.
"He was the one guy coming out of spring late, not as many appearances as the other guys, so we were kind of spoon-feeding him into a more prominent role," Melvin explained. "He just gives us another option late in games, and we have a lot of them."
Jane Lee is a reporter for MLB.com. Read her blog, Major Lee-ague, and follow her on Twitter @JaneMLB. This story was not subject to the approval of Major League Baseball or its clubs.