Peterson, who turned 32 last month, became a free agent when the Minnesota Vikings decided not to pick up their $18 million option on him.
Butler has played in 43 regular-season games with 33 starts, including starting all 16 games in each of the last two seasons for the Patriots. The team's leading rusher has had fewer than 160 touches in five of the last seven seasons.
If Peterson joins the Saints, he might have to share the rushing load with Mark Ingram, a former Heisman Trophy victor who ran for 1,043 yards last season.
The Vikings signed Long last October after they had lost tackles Matt Kalil and Andre Smith to season-ending injuries. And how do you feel about New Orleans being the Minnesota Vikings first regular season opponent during the 2017 season? So it's doubtful after Saturday there'll be many, if any, teams willing to pay so many millions a year for a reliable runner, when most draftees come far cheaper. The source told Yahoo Sports that Peterson likes the city of New Orleans and the proximity to his offseason home in Texas, allowing him to potentially finish his career close to family.More news: Crowds 'March for Science' in global Earth Day protest
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The Vikings announced February 28 they would not pick up Peterson's $18 million contract option for 2017. Peterson totaled 72 yards on 37 carries.
The biggest hesitation I have is that Payton himself has repeatedly lauded the depth of this year's running back class in the middle rounds of the draft.
However, the Saints have developed cold feet and a trade before Thursday's 2017 National Football League draft now seems unlikely, according to a report.
The 6-foot-1, 238-pound Compton registered a career-high 104 tackles (60 solo) in 2016 - his third full season with the Redskins.