"If Kenji does well tonight and catches nine innings, or close to that, we'll probably bring him in tomorrow, have him travel [to L.A.] with us and activate him before the first game [against the Dodgers on Friday night]," manager Don Wakamatsu said.
Johjima, sidelined since May 25 with a broken left big toe, played seven innings on Tuesday night, had two hits and no problems with the toe.
Johjima's return likely would lead to Burke's departure.
"It's tough, especially leaving this type of team," Burke said. "Guys are having a lot of fun. It's great to be a part of that. I know decisions have to be made and if it's me, which it looks to be, I will go back to Tacoma, work hard and hopefully get an opportunity to come back and help these guys as much as possible to reach the postseason."
The Mariners went into Wednesday night's game just 2 1/2 games behind the Rangers and Angels, who were tied for first in the AL West.
If Burke is the other half of the roster shuffle that opens a spot for Johjima, he must be designated for assignment, giving the team 10 days to trade, release or outright him to the Minor Leagues. He must also clear a 72-hour waiver period, which exposes him to the other 29 MLB organizations.
Burke made it through waivers unclaimed earlier this season and figures to make it through waivers again, which would lead to his return to the Rainiers.
"You have to deal with whatever happens, take it in stride and keep working hard," Burke said.
Burke said he would return to his offseason home and work out with the Roseburg American Legion team and perhaps do some fishing during the 10-day period.
"It's not like a vacation," Burke said, smiling. "You have to work out and stay in shape."
Burke started the season with Tacoma and was promoted on April 16 when Johjima went on the 15-day disabled list with a strained right hamstring. Burke started four games, went 1-for-13 and returned to the Rainiers on April 30 when Johjima was activated.
Burke replaced Johjima again on June 7, has started eight games and gone 4-for-28.
"Time flies so fast when you're up here," Burke said. "It seems like I got here yesterday."