The reigning league most valuable player said he would pass Smith during the 2017 season, and even has a date in mind, according to the Minneapolis Star-Tribune.
Peterson, 28, rushed for 2,097 yards last season, eight yards fewer than Eric Dickerson's single-season rushing record of 2,105. His goal for this season is to reach 2,500 yards.
As for Smith's mark of 18,355 yards, Peterson told the paper that he can get there by Week 16 of the 2017 season, well ahead of his current pace of Week Four of 2019.
Peterson currently has 8,849 yards. By his estimate, he would need to average 120.3 yards per game over a 79-game span to collect the 9,507 yards needed.
"Whoo. That's pushing it, huh? But hey, pushing it is the only way to do it. You know it," he told the Star-Tribune.
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With 215 receptions and 25 touchdowns in his first three seasons, New Orleans Saints fourth-year tight end Jimmy Graham has clearly out-performed the rookie contract he signed in 2010 and will likely become the highest-paid tight end either this fall or next spring.
But while some players in his situation would have at least been tempted to hold out and skip training camp to get a contract extension to ensure his long-term financial security, Graham reported on time last week.
Graham is scheduled to earn $1.323 million in base salary this season after making $540,000 a year ago.
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While New England Patriots coach Bill Belichick continues to dance around how he will employ Tim Tebow, the former Heisman Trophy winner appears to be settling in at quarterback.
"Ninety-nine per cent of Tebow's activity during his time with the Patriots has been spent learning to play quarterback in the team's system," writes the BostonGlobe's Ben Volin.
"He has only spent time in the quarterback meeting room, he wears a red non-contact jersey on the field and he runs the third-team offense during team drills."
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The injured foot of Buffalo Bills defensive end Mario Williams seems to be a growing concern.
He sat out Sunday's practice because of that injury, and on Monday, he left training camp to have the foot examined.
"He's going to be evaluated by our doctors, so he's off campus being evaluated," head coach Doug Marrone said, according to The Buffalo News. "I have not heard any report yet.
Williams is entering the second year of his $96 million contract. He had 10.5 sacks for the Bills last season.