Staley, who will receive $17.4 million in the deal, will net a raise from $5.5 million to $8.72 million this season, per the report.
While the move does little in terms of the 49ers' salary cap, it could be construed as a show of good faith while influencing the 33-year-old Staley to stick around with quarterback Jimmy Garoppolo for the next two years instead of contemplating retirement.
Garoppolo signed a five-year, $137.5 million contract in February. He has won all five of his starts with the 49ers since being acquired in a midseason trade with the New England Patriots in 2017 in exchange for a 2018 second-round draft pick.
Garoppolo received a strong endorsement from Staley, an 11-year veteran and six-time Pro Bowl selection.
"The way he came into the huddle and practice when he was there for two days and really just kind of took over," Staley told SiriusXM NFL Radio in February. "He was kind of snapping at guys, 'Hey, pay attention. This is what we're doing right here.' There was no kind of feeling-out period with him. He did it in a way too where it didn't come off as arrogant or anything like that. It was just like I'm asserting myself. This is what we need to do.
"I think a lot of that comes from who he was job shadowing for the first three or four years of his career over there in New England."