According to the Yahoo report, Johnson would earn $500,000 for his fifth start, $1 million for his 10th, $500,000 for his 15th, $1 million for his 20th and $250,000 for every start from Nos. 21-33.
Johnson signed a one-year, $8 million deal with the Padres last offseason but missed all year after undergoing Tommy John surgery in April. San Diego declined a $4 million option for 2014 this offseason, but both parties were interested in giving it another go.
"With Josh, he's a guy that everyone has a positive feel for," Padres general manager A.J. Preller said at the end of the regular season. "We'll try to go down the road with him and try to present something to him that makes sense to him."
The 30-year-old Johnson has been one of the game's most dominant starters when healthy. He earned All-Star nods in 2009 and '10 with the Marlins and posted a 2.30 ERA over 28 starts in '10. He was 8-14 with a 3.81 ERA in 31 starts in 2012, but made only 16 starts in 2013 for the Blue Jays because of injuries.
He's hoping to return to form in San Diego after being unable to do so last year.
"I look at [my time in San Diego] as unfinished business," Johnson said. "It's been very tough to sit here and watch it all. But I think I've actually learned more this year than any other year in the past put together.
"And as far as the organization goes, I couldn't have hoped for anything better. They've been amazing. Not just the training staff, either. But everyone here ... there's been a lot of support."
Johnson started his throwing program in October and the normal Tommy John recovery period -- 12-18 months -- could possibly mean a midseason return. This was his second Tommy John surgery. He underwent the first in 2007 at age 23.
He is 58-45 with a 3.40 ERA in 170 games (160 starts) in nine Major League seasons.
Cash Kruth is a reporter for MLB.com. Follow him on Twitter at @cashkruth. This story was not subject to the approval of Major League Baseball or its clubs.