Allen was listed as questionable for the game on the injury report, while the Bills opted not to elevate third-string QB Matt Barkley to the active roster.
The MVP candidate, who has led Buffalo's offense with 2,403 passing yards for 19 touchdowns along with 392 rushing yards and four other scores on the ground this season, was limited at Friday practice having picked up the elbow injury late in Sunday's loss to the New York Jets.
Allen has only participated in one day of practice this week, having sat out on Wednesday and Thursday but Bills head coach Sean McDermott remained bullish.
"We are literally in an hour-to-hour situation here just looking at how he's going to progress through the day," McDermott told reporters on Friday.
"As he goes through these different tests, medically, making sure that he's able to check the boxes in a progression to where we can see if we can proceed through the course of the day here."
ESPN has reported that Allen's specific concern is an ulnar collateral ligament, related to nerves, in his right elbow. Allen missed four games in the 2018 season with a similar injury to the same arm.
Case Keenum is Allen's back-up QB and he has spoken about being prepared to play if required this week.
"At the end of the day, Josh needs to be Josh, if he's able to play," McDermott added. "And if Case plays, then Case needs to be Case and run the offense."
The Bills are 6-2 and atop the AFC East division, while the Vikings are 7-1 and clear on top of the NFC North on the back of a six-game winning run.
Buffalo lost to the Kansas City Chiefs 42-36 in overtime in the divisional playoffs last season.