Without citing sources, the newspaper said it confirmed team owner Zygi Wilf will announce Frazier as the eighth head coach in Vikings history Monday or Tuesday in a three-year deal.
The Washington Post reported Frazier said he intended to speak to the team's owners Sunday night or Monday.
"Nothing has been solidified," Frazier said. "We're going to talk further.
"I'd love to be in that role next season. ... I'm hoping for the best and believing I'll be back in Minnesota."
Frazier took over from the fired Brad Childress Nov. 22 when the team was mired in a 3-7 start and since guided the Vikings to a 3-3 record despite turmoil and distractions.
Despite a season-ending 20-13 loss at Detroit Sunday, the newspaper said the team was impressed by the way Frazier handled such challenges as the collapse of the Metrodome roof and a league decision to push last week's game between the Vikings and Eagles to Tuesday because of a blizzard in Philadelphia.
The team also had to deal with the loss of quarterback Brett Favre to injury and an NFL investigation into allegations he sent sexually oriented messages and photos to a New York Jets employee when he was with that team.
Scarlett Johansson steps out with fiance after pregnancy reveal
Susan Sarandon 'very excited' about daughter's pregnancy