The deal is the maximum the Spurs were allowed to offer Ginobili under the current collective bargaining agreement, based on Ginobili's current salary and age (32).
A league source said Thursday that the extension only needs league approval and is expected to be finished Friday.
Before the Spurs' game Wednesday night against the Phoenix Suns, Ginobili said he's "closer than ever" to an agreement. He added reports the deal is done are premature.
"We're still working on a couple of details and stuff but we've made a lot of progress," he said, "and I'm happy about it."
Whatever concerns the Spurs might have had about Ginobili's injury issues in the past few seasons have been allayed by his performance the past two months.
Ginobili said he has been physically fine since the start of the season, but that he had "a mental issue" to overcome about finishing around the rim.
Ginobili has been with San Antonio since 2002. He's averaging 16.6 points and 5.6 assists per game this season.
"He's playing [like] he did when we won championships," Popovich said. "He had a tough first half of the year for a variety of reasons, but he's been an All-Star player the last month or month and a half. That's really helped our team come together, especially with [Tony] Parker being down."
He could have become a free agent after the 2010 season ends for the Spurs, who are tied for sixth in the Western Conference standings entering Friday's games.
Ginobili's value to San Antonio is heightened by the fact that as a Spanish-speaking Argentine, he is immensely popular in San Antonio's Hispanic-rich market.
Ric Bucher is senior NBA writer for ESPN The Magazine. Information from The Associated Press contributed to this report.