Suzuki had three hits in Seattle's 9-5 loss to Oakland on Saturday, moving within one of the 2,000 mark.
As long as he gets one hit in his next 12 games, Suzuki, who has played in 1,401 games with the Mariners (72-65), will become the second-fastest to reach that mark. Al Simmons did it in a record 1,390 games, while George Sisler is currently second on the list at 1,414.
"We have a lot of games left to play, a lot of more baseball left in the season," Suzuki told the Mariners' official Web site. "If there were only four or five games, then I would be naturally conscious about it, but as of now, I'm not."
Suzuki is also six hits away from his ninth consecutive 200-hit season, which would break the mark he currently holds along with Willie Keeler (1894-1901).
That achievement looked like it might be moderately challenging for Suzuki to reach when he was held out of Seattle's lineup for eight games last week to nurse a calf injury, but the two-time AL batting champion hasn't missed a beat since returning to the lineup.
He is 10 for 22 (.455) in five games since his return, and has hit safely in 18 of his last 19 games overall. The nine-time All-Star is also batting .442 in nine games against the A's (60-76) this season and is 2 for 5 lifetime against scheduled starter Gio Gonzalez (4-5, 6.07 ERA).
Seattle, which has won nine of 13 despite Saturday's loss, is 11-4 versus Oakland this season.
Mariners rookie Doug Fister (2-1, 2.94) looks for a second straight impressive outing when he makes his sixth career start.
After being tagged for five runs and five hits - including three homers - in six innings of an 8-4 loss to weak-hitting Kansas City on Aug. 27, Fister stymied the AL West-leading Los Angeles Angels on Tuesday. The right-hander limited one of the majors' top offenses to one run and five hits in a career-high 7 1-3 innings of a 2-1 win.
"We'll continue to watch (Fister), but at least he's proven that he can get some awfully good hitters out, and that's a heck of a starting point," Seattle manager Don Wakamatsu said.
This will be Fister's first career outing against the A's, who have lost 11 of 18.
Gonzalez is 0-3 with a 7.29 ERA in his last four starts after going 3-0 with a 1.46 ERA in his previous four. Walks have been the biggest problem for the rookie left-hander, who has issued 17 base on balls in 21 innings over his last four outings.
Against Kansas City on Monday, Gonzalez permitted five runs, six hits and four walks in 5 1-3 innings and did not receive a decision in Oakland's 8-5 victory.
Gonzalez lost at Seattle on Aug. 26, when he gave up four runs, seven hits and three walks in five innings of a 5-3 defeat.Sign up for breaking news alerts from FOXSports.com!